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DR. McCOSH'S WORKS. 



FIRST AND FUNDAMENTAL TRUTHS. Being a Treatise on Metaphysics. 
$2.00. 

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THE 



Laws of Discursive Thought 



& textbook of jformai Eogtc 



BY 



JAMES McCOSH, LL.D. 

EX-PRESEDENT OF PRINCETON COLLEGE 






REVISED EDITION 

/&rfS n/ 



NEW YORK 
CHARLES SCRIBNER'S SONS 

1891 






Entered according to Act of Congress, in the year 1870, by 

ROBERT CARTER & BROTHERS, 

In the Clerk's Office of the District Court of the United States for the 
Southern District of New York 



Copyright, 1891, 
By Charles Scribner's Sons. 



THE LIBRARY] 

OF CONGREIf j 

^ASHlNGTOffj 



Presswork by 
John Wilson and Son, Cambridge, U.S.A. 



PREFACE. 



If we look back half a century we find Formal 
Logic taught in nearly all the colleges of Great 
Britain and America, but exercising an influence infi- 
nitely less than nothing (to use a phrase of Plato's) on 
the thought of the countries. Some of the professors 
and tutors were expounding it in a dry and technical 
manner, which wearied young men of spirit, and bred 
a distaste for the study ; while others adopted an 
apologetic tone for occupying even a brief space with 
so antiquated a department, and threw out hints of a 
new Logic as about to appear and supersede the old. 
The lingering life maintained by that old Aristotelian 
and Scholastic Logic, in spite of the ridicule poured 
upon it by nearly all the fresh thinkers of Europe for 
two or three centuries after the revival of letters, is 
an extraordinary fact in the history of philosophy ; I 
believe it can be accounted for only by supposing 
that the syllogism is substantially the correct analysis 
of the process which passes through the mind in rea- 
soning. Certain it is that no proffered logical system 
has been able to set aside the Aristotelian, whether 
devised by Ramus, by the school of Descartes, the 
school of Locke, or the school of Condillac ; all have 



iv PREFACE. 

disappeared after creating a brief expectation fol- 
lowed by a final disappointment. It is a remarkable 
circumstance that the revived taste for Togical studies 
in the last age proceeded from a restoration of the 
old Logic by two distinguished men, both reformers 
in their way, but both admirers of the Analytic of 
Aristotle. I refer to Archbishop Whately and Sir 
William Hamilton. 

Whately first gave his views to the public in an ar- 
ticle in the Encyclopcedia Metropolitana, which was ex- 
panded into his Elements of Logic in 1826. The pub- 
lication constitutes an era in the history of the study 
in Great Britain and America. The admirable defence 
of the old Logic against the objections of such men 
as Principal Campbell and Dugald Stewart, and still 
more, the fresh and apt examples substituted for the 
dry stock ones which had been in use for a thousand 
or two thousand years, speedily attracted the favor- 
able attention of the young thinkers of the times ; and 
Aristotle was once more in the ascendant. But while 
Whately's Elements is an interesting and healthy 
work, it can scarcely be described as specially a 
philosophic one. In order to complete the reaction, 
another thinker had to appear, and subject the whole 
science to a critical examination fitted to satisfy the 
deeper philosophic mind of the times. It is a curious 
circumstance that Hamilton uttered his first oracular 
declarations on Logic in a severe article on Whately, 
in the Edinburgh Meviezv, published afterwards in his 
Discussions. He embraced the opportunity to bring 
forth the result of his profound researches, and spe- 
cially to introduce to the English speaking countries, 
the Logic which had sprung up in Germany out of 



PREFACE. V 

Kant's Critick of Pure Reason. Since that date, 
Logic has had a greater amount of interest collected 
round it in Great Britain than any other mental 
science, and has become incorporated with the fresh- 
est and brightest thought of the country. The in- 
terest in the study has been increased by the Logic of 
Mr. John Stuart Mill, who has evidently felt the in- 
fluence of Whately in the respect which he pays to 
Formal Logic, but adheres, as a whole, to the princi- 
ples of his father, Mr. James Mill, introducing some 
elements from the cognate Positive Philosophy of M. 
Comte. Mr. Mill has given an impulse to the study, 
not by the portion of his work which treats of Formal 
Logic — which is not of much scientific value — but by 
his valuable exposition of the Logic of Induction, 
which would have been of much more value had he 
left out the constant defences of his empirical meta- 
physics. 

The New Analytic proceeds directly or indirectly 
from the metaphysics of Kant. Not that it is to be 
found developed in the works of Kant, but it is largely 
grounded on the peculiar principles of the Critioh of 
Pure Reason ; it rose out of the searching criticism to 
which Kant had subjected the forms of the Old Logic ; 
and it ramified directly from the logical treatises of 
such men as Krug and Esser who belonged to the 
school. It is of a composite structure, resembling the 
renovations we see in Britain of mediaeval buildings, 
the old and the new adapted to each other with won- 
derful skill, but with an occasional incongruity forcing 
itself here and there on the notice of the careful ob- 
server. I am not convinced that all the parts are 
likely to be preserved in the shape they now have, or 



vi PREFACE. 

that the Analytic always gives the ultimate expres- 
sion of the laws of thought ; but I am sure it is a valu- 
able accession to the science. Altogether independ- 
ent of its positive improvements, it has done great 
service, by the careful examination to which it has 
subjected the Old Logic — which has come creditably 
out of the trial. Forms which had become venerable, 
and, I may add, stiff, from age ; and which were 
inclined to stand on their dignity and acknowledged 
authority, have been obliged to submit to a sifting 
scrutiny, which may have shorn them of some of their 
ridiculous pretensions, but has, at the same time, de- 
livered them from the dry dust which had gathered 
around them and threatened to bury them. The time 
has now come for subjecting the New Analytic to a 
like examination. It has been before us for an age 
in a half developed form, and for half an age in a 
fully unfolded shape ; and we should now be in a suf- 
ficiently impartial position to be able to take from it 
what is worthy of being retained, and to lay aside 
what is fallacious or mistaken.* 

The defects and errors of the new Logic are de- 
rived mainly from its German paternity. It is in- 
fected throughout with the metaphysics of Kant — just 
as the Art of Thinking is with the metaphysics of 
Descartes, and Mill's Logic with the empiricism of 
Comte. It ever presupposes, or implies, that there 
are Forms in the mind which it imposes on objects as 
it contemplates them ; and it makes the science alto- 
gether a priori, and to be constructed apart from, 

* I believe copies may be had of a limited edition of Philosophic Papers pub 
lished by me, and in which I examined Hamilton's Logic. 1 have reviewed 
Mill's Logic in my Examination of Mr. J. S, Mill's Philosophy. 



PREFACE. vii 

and altogether independent of experience. Hamilton 
quotes (Logic, Led. IV.) Esser with approbation. " It 
is evident that in so far as a form of thought is neces- 
sary, this form must be determined or necessitated by 
the nature of the thinking subject itself. . . . The first 
condition of a form of thought is that it is subjec- 
tively, not objectively, determined." This fundamen- 
tal error (so I reckon it) runs through the whole 
system, and injures and corrupts the valuable truth 
to be found in the Logic of Hamilton. \ I acknowledge 
that there are principles or laws in the mind, original 
and native ; but these do not superinduce or impose 
forms on objects as we look at them ; they simply 
enable us to perceive what is in the objects. \ True, 
there are a priori laws in the mind operating prior to 
experience ; but we can discover their nature, and give 
an accurate expression of them, only by means of care- 
ful observation. The science of Logic is to be con- 
structed only by a careful inductive investigation of 
the operations of the human mind as it is employed 
in thinking. 

In conducting my independent researches in this 
spirit, I have been thrown back on the old Logic 
more than even the logicians of the school of Kant 
have been. But I have been obliged, in order to 
explain certain operations of thought to which Kant 
and Hamilton have called attention, to unfold laws 
which were not noticed by the older logicians. 

The main feature of this Logical Treatise is to be 
found in the more thorough investigation of the na- 
ture of the Notion, in regard to which the views of 
the school of Locke and Whately are very defective, 
and the views of the school of Kant and Hamil- 



viil PREFACE. 

ton altogether erroneous. The Port Royal Logic 
complains that the part of Logic which comprehends 
the rules of reasoning is regarded as the most impor- 
tant ; and maintains that the greater part of the 
errors of men arises from their reasoning on wrong- 
principles, rather than from their reasoning wrongly 
from their principles. It is as true of this age as of 
the seventeenth century, that the attention of logicians 
has been confined almost entirely to Reasoning. I 
believe that it is the Notion which requires at this 
time to be specially examined. I believe that errors 
spring far more frequently from obscure, inadequate, 
indistinct, and confused Notions, and from not pla- 
cing the Notions in their proper relation in Judgment, 
than from Ratiocination. Even in Reasoning, most 
mistakes proceed from confusion lurking in the Ap- 
prehensions of the mind. We are in more need, at 
present, of a new analysis of the Notion and the 
Judgment, than of the Reasoning process. I have 
found that in the more thorough evolution of the 
nature of the Notion, especially in the thorough-going 
separation of the Abstract Notion from the Singular 
and Universal, we have the means of settling the 
curious questions which have been started in regard 
to Judgment and Reasoning in the New Analytic. In 
this treatise, the Notion (with the Term, and the 
Relation of Thought to Language) will be found to 
occupy a larger relative place than in any logical 
work written since the time of the famous Art of 
Thinking. 

Princeton, New Jersey, U. S., 
April, 1S70. 



PREFACE TO REVISED EDITION. 



Much more attention is now paid to Logic than for 
several years prior to the time when I published this 
work. It is now seen that Formal Logic is the most 
certain science next to Geometry, and is more emi- 
nently fitted than any other branch of study to give 
accuracy to thinking. It is especially needed in the 
present day, when there is so much largeness, but at 
the same time so much looseness of thinking, which 
is to be restrained and corrected by the science which 
treats of the precise nature of thought. 

It is well known that our science consists of Simple 
Apprehension, Judgment, and Reasoning, or, in other 
words, of the Notion, the Proposition, and the Argu- 
ment. I am confirmed in the opinion that in the 
present day, of the three Parts, that most needing to 
be expounded is Apprehension or the Notion. Upon 
this the Judgment and the Reasoning largely depend. 
Error in thinking proceeds much more frequently and 
extensively from inadequate and confused Notions 
than from mistaken judgments and reasoning. More 
than one half of erroneous propositions and argu- 
ments spring from misapprehension and looseness in 
our ideas. I have, therefore, taken immense pains to 



X PREFACE. 

explain the nature of the various kinds of Notions, 
and to furnish a correct analysis and division of 
them. I have explained the relation of Language to 
Thought. 

I may mention some other peculiarities of this 
treatise : — 

Under Judgment I have explained the distinction 
between Substitutive (Convertible) and Attributive 
(Inconvertible) Judgments, and have given a full ex- 
position of Implied Judgments or Immediate Infer- 
ences. 

Under Reasoning I have enunciated the Regulating 
Laws of all ratiocination. 

In closing, I have unfolded the Fundamental Prin- 
ciples which underlie Discursive Thought. I have 
appended exercises to help us to secure accurate 
thinking. 

I have excluded the process of Induction from 
Formal Logic, that it may be placed under the sepa- 
rate head of Inductive Logic. But I have shown that 
there is Reasoning involved in rising from the scat- 
tered observed facts to the law, and how the Reason- 
ing may be put in syllogistic form. 

The tendency of German thinkers from the days of 
Hegel has been to extend the province of Logic, and 
to make it embrace the theory of knowledge and much 
that is properly metaphysical. I think it of vast mo- 
ment to restrict it to its own field, which is that of 
Discursive Thought, and thus keep one great science, 
established by Aristotle, from endless speculation. 

Princeton, N, J., May, 1891. 



TABLE OF CONTENTS. 



INTRODUCTION, 

SUCTION PAGB 

t— 5.— Definition of Logic 1 

6 — 7.— Division of the Science 2 

FOEMAL LOGIC. 
8— 11.— The Notion, Judgment, and Eeasoning 4 



PART FIRST. 
THE NOTION. 

1.— Definition of Notion 1 

2.— The Term ? 

3. — All Notions either Concrete or Abstract 8 

CONCRETE AND ABSTRACT NOTIONS. 

4 — 6. — Nature of Concrete and Abstract Notions 8 

7.— The Phantasy ... 10 

8 — 9. — Abstractions from Concretes and other Abstractions 10 

10.— Comprehension of Abstract Notions 12 

LAWS OF THOUGHT INVOLVED IN ABSTRACTION. 

11.— The Abstract implies the Concrete 12 

12.— When tlie Concrete is Real the Abstract is Real 13 

13.— An Attribute has no Independent Existence 14 

14.— The Reality in the Abstract Notion 15 

IS — 17.7^Importance of Abstraction 16 

SINGULAR AND UNIVERSAL NOTIONS. 

18.— All Notions either Singular or Universal 18 

19,— Our Primary Knowledge is of Singulars 18 



Xll 



CONTENTS. 



SECTION TAOB 

20— 21.— Abstraction and Generalization not the same 19 

22.— What is presupposed in Generalization 20 

23.— First Step.— Observation of Resemblances 21 

24 — 26.— Second Step.— Fixing on Points of Resemblance 21 

it.— Third Step.— Formation of a Class 23 

28. — A Universal, wherein Indefinite, wherein Definite 2S 

LAWS OF THOUGHT INVOLVED IN GENERALIZATION. 

29. — The Universal Implies Singulars 24 

30.— When Singulars are Real the Universal is Real 25 

31.— The Reality of the Universal is in Common Properties of Singulars 25 

EXTENSION AND COMPREHENSION OF GENERAL NOTIONS. 

32 -33.— A General Notion embraces Objects (Extension), and Attributes 

(Comprehension) 26 

HIGHER AND LOWER GENERALIZATIONS. 

34.— Common Notions with an aggregate of Attributes 27 

35.— Genus and Species 28- 

36.— It is Implied that the same Objects are Generalized 29 

37.— Co-ordinate, Subordinate, and Communicant Species 29 

SINGULAR CONCRETE, ABSTRACT AND UNIVERSAL NOTIONS. 

38— 39.— Explanation of this Threefold Division 29 

40. — The Singular Concrete, or Percept 30 

41.— The Abstract Notion or Abstract 31 

42. — The Universal Notion or Concept 31 

43. — Distinction between Generalized Abstract and Generalized Con- 
crete 32 

44.— The General Abstract 32 

45. — The General Concrete 32 

46. — Admits of Higher and Higher Generalizations 33 

47.— Relation of General Concrete to Natural Classes 33 

MIXED NOTIONS. 

48.— Singular Terms Proper. Singulars Classified. Collective. Sin- 
gulars Abstracted 34 

49. — Terms both Abstracts and Concepts, (Denotation and Connota- 
tion) 35 

50. — Abstract Notions becoming General 36 

51.— Mixed Modes of Locke 37 

52. — All Notions are Percepts, Abstracts, or Concepts 37 

53.— Privative Notions 38 

54. — Contrary and Contradictory Notions 30 

55. — Relative and Correlative Notions 39 



CONTENTS. xiii 

SECTION TAGE 

LOGICAL DIVISION. 

56.— Its Nature 39 

57. — First Rule. — We must proceed according to Marks 40 

58. — Second Bule. — The Species must make up the Genus 41 

59. — Third Bule. — The Members must exclude one another 42 

60—61.- Fourth Bule.— There should be a due Subordination 43 

ANALYSIS AND SYNTHESIS. 

63.— Analysis 41 

63.— Synthesis 45 

64. — Purpose served by Analysis and Synthesis 4S 

LOGICAL DEFINITION. 

65.— Its Nature 46 

66. —Distinguished from Description 46 

67.— Definition of Abstract Notions 46 

68. — Notions which cannot be defined. . . 47 

69. — Definition of General Notions 47 

70.— Bule First. — Bring out a Distinguishing Attribute 48 

71.— Definition of General Concrete Notions 48 

72. — Bule Second.— The Definition must be Adequate 49 

73.— The Test of a good Definition 49 

14i.—Bule Third.— Give the Genus and Differentia 49 

75.— Practical Rules 50 

AIDS TO ABSTRACTION AND GENERALIZATION. 

76. — Need of a Sign of some kind , 50 

I.— Mental Image, or Phantasm. 

77.— Nature of such 50 

78. — Difference between Phantasm and Abstract and General Notion. 51 

79. — Criticism of Locke's views hi 

II.— Language. 

80.— Advantage op Language as an Instrument of Thought 53 

81. — (1) A Sign and Register of Abstractions and Generalizations 54 

82. — (2) Puts us in possession of Abstractions and Generalizations 55 

83—85. — Character of a people shown in their Language 56 

86.— Advantage of being acquainted with more than one Language . 58 

87. — Benefit got by our tongue from other tongues 59 

88— 90.— (3) Gives a form to Thought . 59 

91.— How it may restrain Thought 61 

92— 94.— (4) Lightens Thought by being used as a Symbol 65 

95.— (5) Enables us to carry on Thinking to a greater extent 64 

96— 97.— Men can reason without Language 65 

98—101 —But are always the better of Language 67 



xiv CONTENTS. 

SUCTION PA OB 

102.— (6) Helps Thought to make Progress 69 

103 — 105.— Incidental Disadvantages op Language 70 

IOC— (1) The vagueness of so mauy phrases 72 

107— 110— (2) Different Meanings of the same Word 73 

111. — (3) Misleading Associations 76 

112 Words derived from Matter applied to Mind 77 

113.— (4) We use Words without inquiring into their Meaning 77 

114.— How are the E vils to be avoided 78 

(1) Ascertain the Meani ng of the Word 79 

115.— (2) When Ambiguous ascertain the Various Meanings 79 

116. — (3) Determine the Notion for which it stands 79 

117.— (4) Ask whether the Notion is Singular, Abstract, or Universal. . . 80 

118.— Especially in Abstruse Thinking 81 

119.— (5) Consider the Things from which the Notions are formed 83 

LAWS OP THOUGHT INVOLVED EN USE OF SIGNS. 

130. — First Law. — A Term stands for a Notion, Singular, Abstract, or 

Universal 83 

121.— Second Law.— We can Predicate of Sign only what can be Predi- 
cated of Notion 84 

122.— Third Law.— We may demand that the Notion be substituted for 

Sign 84 

HI. — Classes in Natube. 

123— 125.— There are such Classes 88 

106— 127.— Classes called Kinds 88 

128. — Are Aids and Guides in Generalizing 89 

REALISM, NOMINALISM, AND CONCEPTUALISM. 

129 — 132. —Brief History and Criticism of Opinions 90 



PART SECOND. 
JUDGMENT. 

1.— Definition of Judgment <J8 

CATEGORICAL PROPOSITIONS. 
-Subject, Copula, and Predicate 93 



—Nature of the Copula 94 

— Modals 98 

—In Quality, either Affirmative or Negative........ 95 

—In Quantity, either Universal or Particular 95 

Meaning of words 'All' and 'Some' 96 

Indefinite or Indesignate Propositions . ... 98 



CONTENTS. xv 

SECTION PAGE 

9. -Fourfold Division of Propositions, A, E, I, O 96 

10.— Distribution of Terms 96 

11.— Distribution of Subject and Predicate 97 

18— 13.— Various Eelations between Subject and Predicate 97 

14.— Equivalent Propositions 98 

15.— Propositions in which the Relation is op Extension and 

Comprehension 99 

16. — Inconvertible and Convertible — Substitutive and Attributive 100 

17— 18.— Difference between these 100 

19— 20.— Cases in which Predicate is a General Notion Distributed (U) 101 

21. — Predicables of Aristotle and Porphyry 109 

22.— Should the Predicate always be Quantified ? 103 

23.— Hamilton's Table of Judgments 104 

CONJUNCTIONS OF PROPOSITIONS, CONDITIONALS, AND DISJUNC- 
TIVES. 

24.— Various Conjunctions 105 

25. — Conditionals and Disjunctives 10B 

26.— Conditionals, their Nature 106 

•-J7— 28.— Antecedent. Consequent, and Consequence 106 

29. — Conditionals may be Equivalent or Attributive 107 

80— 31.— Disjunctives, their Nature 107 

IMPLIED JUDGMENTS, OR IMMEDIATE INFERENCES. 

82.— Their Nature 108 

33.— Conversion 108 

34. — Opposition in Equivalent Propositions 109 

35.— Opposition in Attributive Propositions 109 

SQ.—Subalternation 110 

37. — Contrary Opposition Ill 

38.— Contradictory Ill 

^.—Demonstration 112 

40. — In discussion Propositions put as Contradictories 112 

41.— Transposed Propositions obtained by Opposition 113 

42. — Transposed Judgments obtained by Extension 114 

43. — These not applicable to Equivalent Propositions 114 

44. — The Interpretation, of Judgments gives Implied Propositions... 114 

45.— Implied Judgments are obtained by Comprehension 116 

The Interpretation of Marks 115 

46.— Added Maries 115 

47.— Added Subject and Predicate 115 

48. — Summation of Predicates 115 

49. — Privative Conceptions , 115 

50.— Conditional Propositions 117 

Si.— Disjunctive Propositions 117 

52.— Rule as to Distribution of Terms in Implied Judgments 117 

53. — Implied Judgments obtained from " men are responsible " 117 

54.— How Logic aids in Determining the Truth of a Proposition 118 



xvi CONTENTS. 



PART THIRD. 
REASONING. 

MOTION VABl 

1. — The Process in the mind when we reason 120 

2. — The Sameness of the Process 121 

3. — Importance of Analyzing the Process 121 

4.— Difference between Judgment Proper and Reasoning 122 

5.— Involves Three Propositions. The Syllogism 123 

6. — Syllogistic Analysis made by Aristotle 123 

7.— Cannot reason from One Judgment. Enthymeme 123 

8.— Extremes and Middle ; Premisses and Conclusion 124 

RULES APPLICABLE TO EVERT KIND OF REASONING. 

9.— (1) There should be only Three Terms 125 

10— (2) And only one Middle 135 

11. — (3) One Premiss must be Affirmative 125 

12. — (4) If either Premiss Negative, the Conclusion Negative 125 

13.— (5) To prove a Negative, one Premiss must be Negative 125 

14. — What are the Regulating Principles of Reasoning ? 125 

15.— First Regulating Principle. " Notions Equivalent to one and 

the same third Notion equivalent to one another." 126 

16.— The TJnfigured Syllogism of Hamilton 127 

17.— Second Regulating Principle. " Whatever is predicated of a 

Class, may be Predicated of the Members of the Class." 127 

18.— Major and Minor Terms. Major and Minor Premisses 128 

19.— Rules derived from the Dictum of Aristotle ; being 

EULES APPLICABLE TO REASONING IN EXTENSION. 

20.— (1) Middle Term distributed once 128 

21. — (2) Term distributed in Conclusion only when in Premisses 12h 

23.— (3) From two Particular Premisses no Conclusion 129 

23.— (4) K one Premias Particular, Conclusion Particular 130 

24.— These Rules apply only to cases in which there is a Concept 130 

25— 26.— Moods 130 

27.— Figure 131 

28— 29.— First Figure.— Its Special Rules 131 

30— 31.— Second Figure.— Its Special Rules 132 

32— 33.— Third Figure.— Its Special Rules 132 

34— 35.— Fourth Figure.— Is it allowable? 133 

36.— Mnemonic Lines 134 

37.— Reduction 134 

38.— Made by Implied Judgments 135 

39. — Ostensive Reduction 135 

40.— Reductio per lmpossibile 136 

41 . —Immediate Inferences in Mediate Reasoning 137 

12 — 44.— Reasoning in Comprehension 13* 



CONTENTS. xvii 



SUCTION PAGE 

45.— The Two Dicta Combined ; 140 

46.— Hamilton"s Table of Forms of Seasoning 141 

47. — Mill's Theory of Reasoning Process 143 

48 — Reasoning from Plurative Judgments 144 



CONDITIONAL REASONING. 

49. — Its Nature and Rules 145 

60.— Common Forms 146 

51— 63.— Relation of Conditional to Categorical Reasoning 146 

DISJUNCTIVE REASONING. 

54.— Its Nature and Rules 148 

55.— Its Principal Forms 149 

56.— Can be Reduced to Categorical 149 

DILEMMA. 

57.— Its Nature 150 

58.— Its Principal Forms 151 

59.— A Trilemma, etc 151 

60. — Reduction to Categorical Form 151 

CHAINS OF REASONING, SORITES. 

61.— Prosyllogism and Episyllogism 152 

62.— Sorites 153 

63.— Reduced to Series of Syllogisms 153 

GENERAL REMARKS ON REASONING PROCESS. 

64.— We get tbe Premisses from Intuition and Observation 155 

65.— Individual and Combined Observation 155 

66.— Some of the Observational Maxims written out, others not 156 

67. — Some of them Certain, others only Probable 157 

68.— Demonstration, in which the new steps are Intuitive 157 

69.— Experiential or Probable Evidence 158 

70.— Is all that can be had in Practical Matters 160 

71.— Falls under the Dictum of Aristotle, and needs a Major Premiss. . 161 

72 -73. — Reasoning Involved in Induction ; the Canons of Induction ; the 

Major Premiss 161 

74. — When Premisses only Probably True 16? 

75— 76.— Concurrence of Evidence 165 

77.— Whence the Rapidity of Reasoning Process ? r. . . 166 

78.— In what sense are the Truths reached New ? 168 



xviii CONTENTS. 

SECTION PAOB 

FALLACIES. 

79. —Definition of Fallacy 169 

80.— What Logic can do in guarding against Fallacies 169 

8< -How the Heart sways the Head 171 

82.— Division of Fallacies , 172 

83.— Formal Fallacies 172 

Undistributed Middle 178 

84.— Elicit Process of Major or Minor Term 173 

85.— Negative Premisses 174 

86.— Arguments with more than Three Terms 174 

87.— Fallacies of Conditionals. . 175 

88.— Material Fallacies 175 

88— 90.— Ambiguous Terms, especially Ambiguous Middle 175 

91. — Fallacia Accidentis 178 

92.— Equivocation 179 

93.— Oblique Expression 180 

94.— Fallacies of Confusion 180 

95.— Fallacy of Division and Composition 181 

96. — Imperfect Division 182 

97.— Fallacy of Shifting Ground 183 

98.— Fallacia Plurium Interrogationum 184 

99.— Petitio Principii 184 

100.— Syllogistic Seasoning not Petitio Principii 185 

101.— Arguing in a Circle 185 

102.— Ignoratio Elenchi 186 

103.— Proving only part of the Question 187 

104.— Fallacy of Objections 187 

105.— Argumentum ad Hominem 187 

106.— Argumentum ad Populum 188 

107.— Argumentum ad Verecundiam 188 

108.— Argumentum ad Ignorantiam 188 

109.— Fallacy of Pretension 189 

110. — Argument from Consequences 189 

111.— Mistakes as to Onus Probandi 190 

112.— Fallacies of Analogy 191 

113.— Imperfect Enumeration 192 

14.— Non Causa pro Causa 193 

15.— Post Hoc ergo Propter Hoc 193 

16.— Mistaking Sign for Cause 194 

17.— Causa Essendi and Causa Cognoscendi ; Reason and Cause 194 

FUNDAMENTAL LAWS OF DISCURSIVE THOUGHT. 

118. — How they are discovered 195 

119— The Law of Identity 195 

120.— The Law of Contradiction 196 

121 .-The Law of Excluded Middle 196 

122.— The Principle of Equality 196 



CONTENTS. X! X 

SECTION PASB 

123.— The Dictum of Aristotle 19ti 

124.— The Principle of Attribution 197 

125.— The Law of Division 197 

126. —The Principle of Whole and Parts 198 

127.— The Consideration of these belongs to Metaphysics 198 



APPENDIX. 

I.— Exercises as to Forms 

1—7.— The Notion 199 

8— 14.— Judgment 201 

15— 27.— Reasoning 202 

II. — Exercises as to Violations of Laws of Thought 

27— 31— In Notions 207 

82— 35.— In Judgments . 209 

86— 68.— In Reasoning 909 



INTRODUCTION. 



DEFINITION AND DIVISION OF THE SCIENCE. 

1, Logic may be defined as the Science of the Laws ol 
Discursive Thought. The matter about -which it is em- 
ployed lies in the mind : it is Thought, which is an exer- 
cise of the understanding, the intelligence, or the intellec- 
tual or cognitive powers, as distinguished from operations 
of the motive faculties such as emotion, moral perception 
or volition. Thought or intelligence may be of two "kinds. 
In some cases we perceive the object or truth at once : 
as when we see or touch the table before us, as when we 
know that the shortest distance between two points is a 
straight line. In other exercises we perceive the thing or 
truth by a process : from something given we draw some- 
thing else, as when we argue from certain appearances in 
the sky that it will be rain, or from the structure of 
certain strata of the earth's surface that they have been 
formed in water. This second kind of thought is called 
Discursive, in which we proceed from something allowed 
to something else derived from it by thinking ; as dis- 
tinguished from Intuitive Thought, in which we discern 
the truth immediately. The science which treats of the 
intuitive operations of the mind is called Metaphysics ; 
the science which considers the discursive acts is Logic. 

2. The discursive operations, like all other agencies in 
nature, proceed in a regular manner, that is, according to 
laws. By carefully observing the acts of the mind in 



2 INTRODUCTION. 

thinking, we may discover what these laws are, and ex. 
press them in language or in formulae. In doing this, we 
are constructing a science, which is co-ordinated know- 
ledge, as distinguished from the knowledge of individual 
things as they present themselves. As Logic co-ordinates 
what it observes, it is a science ; it is the science of the 
laws of discursive thought. 

3. There is no definition of Logic" in any of the extant writings 
of Aristotle the founder of the science. Of later logicians some 
have given a narrower and some a wider definition than that 
adopted in the text. Some represent it as a pure science ; some as 
a mere art. Some, such as Whately, would have it treat of Seasoning 
exclusively (omitting the Notion and Judgment), while others 
would enlarge it so as to make it embrace all intelligence. The 
definition of the text gives it a rigidly exact field, while it comprises 
all the mental operations embraced under the laws of discursive 
thought. 

4. It should be noted that Logic does not profess to 
impart to man the power of thinking any more than 
Grammar gives him the capacity of speech. Logic finds 
men engaged in apprehending, judging, and reasoning, 
and it seeks to unfold the laws involved, just as Grammar 
presupposes that men can speak, and proceeds to detect 
the rules of correct speech. And as Grammar by its 
rules enables persons to express themselves accurately, 
so Logic by expounding the laws of thought guards 
against mistakes in thinking. So far as Logic unfolds 
the laws of a department of our nature it is a science; so 
far as it supplies rules to guide and guard us in our dis- 
cursive operations it is an art. 

5. As Logic deals with Thought primarily, and looks at Language 
only secondarily and incidentally, it is thus easily distinguished from 
Grammar, Ehetoric, and the Science of Language, which all treat of 
speech, writing or language generally. 

0. Discursive Thought may be viewed in its general 
aspects or in its more special applications. It may be 
contemplated as directed to objects of any kind, no 



DEFINITION OF THE SCIENCE. 3 

matter what they be, within or without us ; or it may 
be considered as looking to certain classes of objects ; 
thus it is evident that thinking is somewhat differently 
employed in mathematical demonstration from what it is 
when arranging objects in natural history. This gives us 
the grand division of the science. So far as it treats 
of discursive operations, whatever be the objects about 
which it is employed, it is called Universal or more com- 
monly Formal Logic. So far as it considers thinking as 
lirected to special kinds of objects, it has been called 
Particular Logic or might be called Objective Logic ; it 
embraces such subjects as Demonstration and Induction. 
This work takes up the former of these. 

7. Kant says, " Logic maybe considered as two- fold : as Logic of 
the general (universal) or the particular use of the understanding. 
The first contains the absolutely necessary laws of thought, without 
which no use whatever of the understanding is possible, and gives laws 
therefore to the understanding, without regard to the difference of ob- 
jects on which it may be employed. The Logic of the particular use 
of the understanding contains the laws of correct thinking upon a par- 
ticular class of objects. The former may be called elemental logic ; 
the latter the organon of this or that particular science. The latter is 
for the most part employed in the schools as a propaedeutic to the 
sciences, although, indeed, according to the course of human reason, 
it is the last thing we arrive at, when the science has been already 
matured and needs only the finishing touches towards its correction 
and completion; for our knowledge of the objects of our attempted 
science must be tolerably extensive and complete before we can 
indicate the laws by which a science of these objects can be 
established. General Logic is again either pure or applied. In the 
former, we extract all the empirical conditions under which the 
understanding is exercised, for example the influence of the senses, 
the laws of the memory, the force of habit, of inclination, conse- 
quently also the sources of prejudice, &c." He tells us, General Logic 
" makes abstraction of all content of cognition, that is of all relation 
of cognition to its object, and regards only the logical form in the 
relation of cognitions to each other, that is the form of thought in 
general." (Critique of Pure Reason, Part II., Meiklejohn's Trans 
lation.) The distinction between Universal and Particular Logic is 



4 INTRODUCTION. 

adopted in the text, but with an important modification. Kant 
makes Universal Logic look at thought apart altogether from content 
or objects, and supposes that the mind has laws or forms which it 
imposes on objects. In the text it is supposed that the laws of 
thought are the laws of the understanding in contemplating objects. 
Formal or Universal Logic treats of thought, not apart from content, 
out whatever be the content, that is, whatever be the objects. 



UNIVERSAL OR FORMAL LOGIC. 

8* Let us look at some of the common exercises of 
Discursive Thought. We have before us a piece of ice. 
So far as we simply look at it, and perceive its form and 
color, there is no discursive thought. But we can distin- 
guish between its form and color, or we may think of its 
qualities, say, its coldness, its brittleness, its transparency ; 
we are now exercising thought upon the object perceived. 
The mere bodily senses can draw no such distinction. 
I can not by the eye separate the shape of the piece of ice 
from its transparency. But on the bare inspection of the 
object the mind can distinguish between it and any of its 
properties, or between one property and another. This 
is Abstraction, a simple and elementary exercise of dis- 
cursive thought. 

0. Again, on looking at two or more objects, we may 
notice that they resemble each other. An inhabitant of a 
northern country is travelling for the first time in a south- 
ern clime, and beholds a plant such as never fell under 
his view before, a plant with a leaf like a fan, and on 
going a little farther he notices another plant of much 
the same general form. Already he is exercising dis- 
cursive thought. He was not doing so as long as he was 
a mere passive recipient of the impression left on the eye 
by the shape and color ; but when he discovers the like- 
ness of the plants he is exercising what is called Com- 



DIVISION OF THE SCIENCE. 5 

parisou. As other like plants fall under his view, he 
will probably take a farther step ; he will form a class 01 
kind which shall embrace not only the plants which he 
has seen, but all others, with the points of agreement, 
. which may fall under his notice or that of any other man ; 
and he will rejoice if some one gives him the name of 
' fan palm ' to designate them. 

The product of these two processes is the Abstract and 
General Notion. The First Part of Formal Logic con- 
siders the Notion, specially the Abstract and General 
Notion. 

10. Suppose now that we have acquired Notions, we 
may proceed to compare them. By a process like that 
described above, the traveller may have formed the 
notion of fig-tree out of specimens of plants of a different 
order growing in the same region, and he may compare 
tne two kinds of objects of which he has the notion, 
and he declares the fig to be of a different shape from 
the palm, and its leaves to be of a different color. "When 
he does so, he is said to be exercising Judgment, which 
is a discursive operation comparing two or more notions. 

The Second Part of Logic treats of Judgment. 

11. But Judgment may be of two kinds. In many 
cases we pronounce a judgment at once on the bare con- 
templation of two notions. It is thus that, considering 
the palm tree and the fig-tree, we discern that the leaf 
veins of the one are parallel, whereas those of the other 
are curvilinear. But in other cases we cannot discover 
the agreement or disagreeraent at once by simply 
considering the notions we have. Thus we cannot by 
merely looking at the palm and fig-tree determine how 
they grow, whether from one seed lobe or two seed lobes • 
whether from within or by adding rings from without. 
But we observe that the veins of the palm leaves are 
parallel, and that those of the fig are reticulated : and we 



6 INTRODUCTION. 

have learned somehow that parallel-veined plants proceed 
from one seed lobe or cotyledon (are monocotyledons), 
and grow from within ; whereas net-veined plants spring 
from two cotyledons (are dicotyledons), and add rings 
without ; and now we are in a position to draw an in- 
ference ; we argue that the palm, being parallel-veined, is 
monocotyledonous, and the fig-tree, having netted veins, is 
dicotyledonous. In drawing these conclusions, we called 
in a third notion, monocotyledous or dicotyledons, to 
combine the other two. The process is one of Judgment ; 
but it is to be distinguished from the second operation 
mentioned above, the Judgment Proper, or what we shall 
commonly call Judgment. In Judgment we compare two 
notions directly, and declare their agreement or disagree- 
ment ; whereas in the process now before us, we compare 
two notions by means of a third. The process is called 
Reasoning, Ratiocination or Inference, and its laws are 
unfolded in the Third Part of Logic. 



PART FIRST. 
THE NOTION. 



1. The operation of the mind in contemplating an ob- 
ject or objects is called Simple Apprehension. The object 
or objects apprehended constitute the Notion. Sometimes 
the notion is of an object apart from any relation to 
others, as ' man ' and ' horse,' and is called Simple or In- 
complex ; sometimes it is of objects in a relation to each 
other, as ' man on horseback,' and is said to be Complex. 
In order, however, to its being a Notion, the mind must 
have brought the objects into a unitj of apprehension. 
' Man on horseback ' is one notion ; we contemplate it as 
one thing. 

2. A notion expressed in language is called a Term, as 
two terms constitute the termini or boundaries of a pro- 
position. A term may consist of one word or of several 
and one word may contain two terms and express their 
connection. A word is said to be categorematic when it is 
capable of being employed by itself as a term, as, for ex- 
ample, nominative nouns, such as horse, dog, deer. Other 
words, such as adverbs, prepositions, and nouns not in 
the nominative case, can only form part of a term, and are 
said to be syncategorematic : thus ' bird on the wing ' 
is one term, though expressed in four words. Again ; 
such words as sum (I am existing), amat (he is loving), 
contain two terms, I and existing, he and loving, and in- 



8 THE NOTION. 

tiraate their relation. In all cases we must look to the 
thought — to the notion in the mind — and not to the mere 
words, to determine what is the notion, and what sort of 
notion it is. 

3» All notions are either Concrete, as ice, or Abstract, 
as coldness. Again, all notions are either Singular, as 
Aristotle, or Universal, as logician. Combining these 
cross divisions we get a three-fold division of notions, the 
Singular, the Abstract, and Universal. It is of great 
importance in Logic that we know the exact nature of 
each of these kinds of notion and the distinction between 
them. Terms are divided as notions are into Singular, 
Abstract, and Universal, which last are usually called 
General or Common (into three, not four kinds, p. 30). 



THE CONCRETE AND ABSTRACT NOTION, 

4, All Notions are either Concrete or Abstract. A Con- 
crete Notion is of objects as they are with an aggregate of 
qualities. An Abstract Notion is of part of an object as a 
part, more technically of an attribute of an object. In 
order to comprehend this distinction we must look at the 
nature of the original cognitions or apprehensions 
which we have by the power of intuition which looks 
immediately on things. In all such we contemplate ob- 
jects with qualities more or fewer, and the notions thus 
formed are said to be concrete. The word is derived 
from con together, and cresco I grow, and means literally 
grown together. Some have derived it from con and 
ierno 3 when it means seen together. Either derivation 
brings out the meaning : in a Concrete Notion the ob- 
jects with their qualities as it were grow together, and 
are perceived together. We cannot look on that table 
without perceiving it at one and the same time as colored 



THE CONCRETE AND ABSTRACT. 9 

and extended : we never can view the color without the 
colored surface, or the surface without seeing it as hav- 
ing color of some kind. Nor can we by any mechanical 
or chemical process separate the one from the other. But 
human intelligence is subtler than any material agent; and 
we can in thought consider the one without taking the 
other into account. This process is called Abstraction, 
from abs from, and traho to draw, and signifies a drawing 
off ; and an Abstract Notion is of a part or a quality or 
qualities drawn off from the rest of the object. 

5. Abstraction may be taken in a wider or a narrower 
sense. In the wider sense it is thus defined by Whately: 
" When we draw off and contemplate separately any part 
of an object presented to the mind disregarding the rest 
of it, we are said to abstract that part of it." Thus under- 
stood, the part abstracted may exist separately : thus if I 
speak of the leg of a table in relation to the table, the 
phrase is abstract ; but I may cut off the leg or consider 
it as it is in itself and without reference to the table, 
in which case our notion is concrete. But abstraction 
may be viewed in a more limited way as that operation 
of mind in which we contemplate an attribute of objects ; 
" by abstract name, I mean the name of an attribute." 
(Mill.) In this sense the thing abstracted cannot be said 
to have a separate or independent existence. Thus I can 
think and reaso.i about the coldness, or transparency, or 
brittleness of ice, but there cannot be coldness or trans- 
parency or brittleness existing separate or apart from the 
ice or an object that is cold, brittle, and transparent. 

0, We may now give examples of each of these kinds 
of Notions. When I think of a stone, the notion is con- 
crete ; but if of heaviness or hardness, the notion is ab- 
stract. If I contemplate a fellow-man, the notion is con- 
crete ; but if I consider his wisdom, or his learning, or his 
wealth, the notion is abstract. If I remember a mother, 



10 THE NOTIOJS 

the mental operation is concrete ; but if I muse on her 
kindness, her care or faithfulness, the process is ab- 
stract. If I contemplate God, the notion is concrete — it is 
God with all his perfections as known to me ; but if I 
meditate on his infinity, his justice, or benevolence, my 
idea is abstract. 

7. In Abstraction taken in the wider sense, we are 
much aided by the phantasy or the imaging power of the 
mind. Having seen an object in its totality I can pic- 
ture to myself a part, provided that part can be separated. 
Thus, having seen a plant, I can have an idea of its roots, 
its stem, its leaves, separately. Having seen a lion, I can 
picture its head and its jaws distinct from the rest of 
its body. But these are exercises of the imaging power 
of the mind, and not of abstraction considered as an act 
of thought. In forming the Notions of attributes, the pic- 
turing power of the mind can be of little service. True, 
when they are of properties of objects perceived imme- 
diately by the senses, it may help us somewhat, thus in 
thinking of transparency, we may have an idea before us 
of glass or of ice ; but when the abstractions are high 
and refined, we can find no image to represent them, and 
any idea we might fashion, would rather have a mislead- 
ing influence, at least in rigid thinking. Who can form 
an idea, in the sense of image, of such abstractions as gov- 
ernment, liberty, peace, prosperity, civilization, religion ? 

8* It is evident that the mind can draw a number, in 
some cases an indefinite number, of abstractions from one 
and the same concrete object. Thus in contemplating a 
rose, we can abstract its form, its color, its odor, its mode of 
growth, its stage of growth, its vital functions, its beauty, 
and I know not how many qualities. From man we ruay 
abstract his bodily frame or any part of it, his shape, his 
size, his reason, his weight, his age, or any of his mental 
attributes, such as his conscience, his feelings, his sinful- 



THE CONCRETE AND ABSTRACT. H 

ness. It would require hours or clays to run over the 
innumerable attributes we might ascribe to such complex 
objects as the Hebrew Commonwealth, the Eoman Empire, 
Greek Literature, the English Language, the Political Con- 
stitutions of Britain and America. The abstractions made 
by any one man in the course of a day, or even an hour, 
are beyond calculation ; and we cannot form the dimmest 
idea of the number fashioned by a man in the course of 
his life, and still less of those formed by all mankind 
since they appeared on the earth. Some of these have been 
embodied in language, but by far the greater number 
never have been and never will be expressed in words. 

9. We cannot have an adequate idea of the process of 
abstraction, unless we take into account that we may form 
abstractions from abstractions, and rise to abstractions 
more and more refined. Perhaps the fittest illustration is 
to be found in the science of numbers. Number of every 
kind is an abstract notion : as one, ten, a hundred, or a 
thousand ; you cannot find one apart from one thing, 
or ten, a hundred, or a thousand apart from ten, a hun- 
dred, or a thousand objects. From these notions we may 
frame higher abstractions as, a, b, c, standing for known 
quantities, and x, y, z, for unknown. A still higher pro- 
cess of abstraction is involved in the Fluxionary and Dif- 
ferential Calculus and in Quaternions. In thus abstract- 
ing it is possible to think of (not to image) an object apart 
from its qualities. This is the farthest point which can 
be reached by us ; that is, we come to the to ov, the Ens 
or Being of which metaphysicians, beginning with the 
ancient Eleatics, have made so much, and yet to so little 
profit, because they have mistaken its nature. When we 
speak of Being, we do not mean that there is any one 
existing thing with a separate or independent reality 
which can be so designated ; but simply to point to an at- 
tribute which all things have, namely, that they exist. 



12 THE NOTION. 

10. When we come to speak of the General Notion, we shall find 
that there is an important distinction between the Extension and 
Comprehension of a Notion. By the Comprehension of a Notion is 
meant the qualities comprised, in it ; by Extension, the objects em- 
braced under it. Abstract Notions may be said, to have Comprehen- 
sion, for they embrace qualities ; and some have more Comprehension, 
that is, more qualities, than others. Thus ' intelligence ' and ' char 
acter,' which include a whole aggregate of properties, is more Com 
prehensive than 'reasoning,' which is only one form of intelligence. 
or 'tamperance ' which is only one element of character. But Ab 
stract Notions can scarcely be said to have Extension, at least as we 
have above defined it. They are apprehensions, not of objects, but 
of qualities of objects. At the same time a quality always is in an 
object, and may be in more or fewer. Thus impenetrability and 
gravity, which are in all matter, are in more objects than fluidity or 
redness, which are only in certain forms of matter. The distinc- 
tion between Extension and Comprehension is one applicable to 
general, rather than abstract, notions. 

From the account now given, the following laws may 
be derived : 

11. First Law, TJie Abstract implies the Concrete. — We 
have seen that the primary knowledge acquired by us is 
of objects with qualities more or fewer. By the eye we 
become acquainted with bodies as at one and the same 
time extended and colored. By touch, we know things 
as at once extended and solid. By self-consciousness, 
we know self as perceiving by the senses, as thinking and 
feeling. Not only so, but when we recall by the mem- 
ory, a scene, a person, an event, it comes before us with 
more than one quality. Even in imagination, the figure 
or scene comes up in the concrete ; we cannot picture to 
ourselves a body with a shape without also giving it 
color, or as having color without also conceiving it a-e 
extended. Proceeding on these concrete ideas, the mind 
can distinguish between a whole and its parts, between an 
object and its qualities, and between one quality and an- 
other. It can consider specialty any one quality of body, 
such as its form, its size, its weight, its density. Tt car 



THE CONCRETE AND ABSTRACT. Yd 

distinguish between man as a whole and any one quality 
of his, such as his bodily strength or stature ; and dis- 
tinguish between any one attribute and another, as be- 
tween his bodily and intellectual power, between his in- 
tellect and his feelings, between any one feeling such as 
joy, and any other feeling such as sorrow. But we are 
not to think that because we can thus distinguish between 
a quality and its object, or between one quality and an- 
other, that therefore the quality can exist of itself. The 
part abstracted implies the whole of which it is a part ; 
in particular the quality or attribute implies an object 
from which it is taken. The question has often been put, 
Is there a reality in the abstract notion, and if so, what 
sort of reality ? The answer is that it has a reality in the 
concrete object or objects, and when it is a quality, as a 
quality of the object or objects. Hence, 

12. Second Law, When the Concrete is Beat the Abstract is 
also Beat. — In laying down this rule it is of course pre- 
supposed that the abstraction has been properly made • 
that is, that we contemplate a real part of a whole, a real 
attribute of an object ; that when we speak of the white- 
ness of a lily, the lily is really white. Let, then, the ob- 
ject be a reality, that is, have a real existence, and the qual- 
ity contemplated has also an existence. True, if the 
objects be imaginary, say a hundred-handed Briareus in 
one body, we cannot declare that these hundred hands 
ever had an existence anywhere except in the imagination 
of the poet ; but if we see a real human being with hands 
before us, we are sure that the hands exist as well as the 
possessor of them ; and if these hands be strong, that the 
strength also is a reality. I can separate in thought the 
beauty of Venus from the person of Venus ; but as the 
person is an ideal creation, so also is the beauty. But, on 
the other hand, if the beautiful person be a living being 
then the form and the color which constitute her loveli- 



14 THE NOTION. 

ness have also an actuality. This proposition is laid 
down in opposition to those who represent all ab- 
stractions as unreal, as imaginary. Some speak of such 
qualities as existence, beauty, virtue, as mere fictions of 
the mind, for which it is vain to seek any corresponding 
reality. It is true all abstractions are creatures of the 
mind, but when we abstract a real part from a real whole. 
a real quality from a real object, the abstract has an 
existence quite as much as the concrete thing. 

13. Third Law, When the Abstract is the property of an 
object, we are not to regard it as having an Independent Exist- 
ence. — Sometimes, indeed, it is a separable part, as the 
root of a plant ; but in this case, when actually separated 
it is no longer an abstract, but concrete. But when it is 
a quality such as color, solidity, weight, thinking, desir- 
ing, revolving, then it is inseparable from the objects, and 
has no independent existence — its existence is simply in 
the objects. Much error has in all ages taken its rise 
from mistaking abstracts for independent wholes. The 
Eleatics very properly formed the abstract notion Being, 
but then they mistook its nature and gave it an existence 
like the objects, say, earth, or gold, or animals which pos- 
sess it. All the Greek philosophers erred, less or more, 
in this respect, giving a separate actuality to the abstrac- 
tions fashioned by their own acute intellects ; and speak- 
ing of ideas, substance, physical elements, as if they were 
agents capable of action like God or individual men. We 
see a like misapprehension among the scholastic logicians 
and theologians of the Medieval Ages ; and their prac- 
tical errors came to have a theoretical sanction giver, them 
by the sect of the Realists, who gave a confused and mystic 
reality to the abstract and general notions formed by the 
mind. The ideal metaphysicians of Germany have in 
much the same way given to Nothing, Something Be- 
coming, a place and a power in themselves. Nor have 



THE CONCRETE AND ABSTRACT. 15 

our modern physical inquirers escaped the tendency, foi 
they speak of nature, force, gravity, motion, as if they 
were entities, acting independently of the objects whose 
action and mode of action they express. 

14:. Corollary. — It is of great importance to trace up 
abstractions to the concrete objects from which they are 
derived. We should thus be saved from the two opposite 
errors into which we are apt to fall : the error of those 
who regard abstractions as nonentities, and that of those 
who give them a distinct being. By following them up 
to the substances, whether mental or material, from which 
they are taken, we shall see that they have a reality, and 
we shall find what is the nature of that reality. Gravita- 
tion has no reality distinct from matter, but it has a 
reality in the stars and planets which it holds in their 
spheres. Nature is not a separate agency, but is a name 
for the combined system of things falling under our view 
in the world. Beauty is a reality, as our esthetic senti- 
ments testify ; but has no embodiment except in some 
beautiful object, though the foolish laudations of some 
might lead us to think that she has a personality of her 
own, which she may one day or other reveal to some en- 
raptured boy-poet, or painter, provided he could rise to 
a sufficiently ecstatic state. Virtue has no separate ex- 
istence in some ethereal sphere, as we might be tempted 
to think by the way in which some speak of it ; but it has 
a reality in the voluntary acts of beings possessed of intelli- 
gence, conscience and free will. The Alexandrian mystics 
recommended us to rise to the contemplation of the One 
and the Good : all very useful and important, we say, 
provided we seek for it, where alone we can find it, in 
the One Living and Good God. 

IS. We cannot close the subject of Abstraction with- 
out pointing out the value and the importance of the 
process. It is involved in all our mental operations which 



16 THE NOTION. 

deserve the name of thinking, and in all practical opera 
tions which require thinking. We cannot speak intelli- 
gently without abstracting, for in speaking about an 
object we separate it from other things. We cannot per- 
form any practical work without such a process, for in 
doing it we must distinguish the things falling simulta- 
neously under our notice. It is an essential element in 
all scientific pursuit ; for in science we have to gather 
the law out of the scattered phenomena of nature, and in 
order to this there must be the " necessary rejections and 
exclusions" (Bacon), that is, the omission of the acciden- 
tal and indifferent. In particular it is by this operation 
we reach those lofty ideas which philosophy ponders. 
We draw off from the objects which present themselves 
to the senses that which is peculiar to the individuals, and 
we have the idea of matter or material substance. In 
contemplating bodies we leave out in our thought al 
other properties except those by which it resists impulse 
and we have the notion of solidity or impenetrability 
From extended body we omit other ideas, and there re- 
mains the idea of pure space. In contemplating ourselves 
and other intelligent beings, we pass by the peculiar- 
ities of the individual, and fixing on the permanent, we 
have the idea of spiritual substance. We separate 
the producing power from the events occurring, and we 
have the idea of potency or causation. We fix on the 
good or bad qualities of moral agents, and we have the 
notion of good and evil. These ideas, matter and spirit, 
substance and quality, space and time, production and 
power, good and evil, are all reached by abstraction, and 
like the primary rocks of our earth, they go down the 
deepest and they mount the highest. Passing beyond 
those qualities that are fleeting, Abstraction goes on to 
those that are fixed ; brushing aside the contingent, it 
reaches the necessary ; and thus discovers the stationary 



THE CONCRETE AND ABSTRACT. 17 

amidst the flowing, the stable at the basis of the tran- 
sient, and the eternal underneath the temporary. The 
mind is thus carried to an elevation where it is above all 
passing occurrences, which it can survey in the thought 
that it is above them, while it feels itself planted on a 
rock which is unmoved amid all mutations. 

10. On the other side, let us not in our search after 
the abstract lose sight of the concrete. Abstract notions 
do indeed serve most important purposes. They have 
been wittily called "the ghosts of departed quantities;" 
they might be more aptly described as the bones, the skele- 
ton, of real bodies. But however essential the skeleton 
may be to the frame, and however important the study of 
it may be for the ends of science, it is not in itself an 
attractive object — except indeed to the anatomist ; — one 
would not just choose to dwell in a chamber full of rat- 
tling bones. For scientific and philosophic purposes it is 
necessary to have abstractions, and these high abstrac- 
tions ; but abstractions cannot promote every good pur- 
pose. In particular they are not calculated to call forth 
feeling or to warm affection into life : it can be shown 
that emotion is evoked, not by abstract notions and prop- 
ositions, but by living objects and concrete apprehensions 
and representations. We do not feel gratitude for ab- 
stract kindness, but for the kind deeds of a kind person. 
Our admiration is excited, not by some grand idea ol 
beauty or sublimity, but by a lovely person or a grand 
scene. Our love is kindled by the contemplation, not of 
goodness (as the pantheist would have it) but by a good 
God or a good man or woman. 

_/7. In order to brace their frame, students should be 
encouraged to mount the heights of philosophy where they 
have a wide and glorious prospect opened to them ; but 
lest, by the cold to which they are there exposed, they have 
the warm current of feeling frozen at the heart, let them 



18 THE NOTION. 

ever be ready to return to what they feel after all to be 
the dearest of spots — the home of the affections. We do 
not wish to find the youth parting with his youthful feel- 
ings ; we do not like to see the young man with the face 
of the old man ; we rather like to see the old man retain- 
ing some of his boyish buoyancy. Our noble English 
tongue has happily been retaining the old Saxon words 
and idioms which furnish " sweet household words and 
phrases of the hearth," while it has been adding to them 
scientific phrases derived from the Greek and Latin lan- 
guages. On a like principle let students, while seeking 
to master the deep abstractions, the high generalizations 
of science and philosophy, cherish their love of the indi- 
vidual, the concrete, the natural : thus only may they be 
able to keep the simplicity of childhood amid the growing 
wisdom of age. 



SINGULAE AND UNIVEESAL NOTIONS. 

IS. All Notions are either Singular or Universal. — A 
singular notion is of an object considered as a single ob- 
ject, as Homer, Virgil, Julius Csesar, Cromwell, Mount 
Blanc, this horse, that dog, yonder mountain. A Univer- 
sal is of objects possessing a common attribute or common 
attributes, the notion being such as to embrace all the 
objects, real or potential, possessing the common attri- 
bute or attributes, as poet, warrior, animal, mountain. 

19. Our primary knowledge is of single objects. The 
boy does not commence with a notion of man or human- 
ity in general, but with an acquaintance with an individ- 
ual person, say his father or his brother ; nor does he 
start with an idea of womankind, but with a kindly know- 
ledge of his nurse or his mother. It is the same with any 



SINGULAR AND UNIVERSAL. 19 

other idea he forms, as of sheep, or cow, or dog ; he first 
notices a single animal, and then as he sees others he 
fashions for himself, or understands as others speak about 
it, the general notion ' animal.' 

20. Abstraction and Generalization, though frequently 
confounded, are not the same. In Abstraction, we sepa- 
rate in thought a part, an attribute, from the whole. In 
generalization, we put objects together as possessing the 
same attributes. In contemplating only one object, we 
can abstract : thus if it be Alexander the Great, we can 
consider his military genius apart from his other quali- 
ities, such as his impulsiveness. But in generalization 
we must always have before us a number of objects which 
we place together by the supposed possession of some com- 
mon attribute : thus in the notion ' conqueror,' we com- 
prise all the great military geniuses of present, past, and 
future time. At the same time the two processes are 
closely connected. Abstraction is always implied in gen- 
eralization : we can combine the objects in the general 
notion only by one or more common attributes, which we 
have therefore abstracted. There may indeed be abstrac- 
tion, the abstraction of a quality, when there is no gen- 
eralization, no combining of objects by the quality. But 
abstraction often leads on to generalization : having ob- 
served a number of rocks which bear marks of having 
been formed in water, we put them in the one class of 
aqueous rocks. 

21. Since the days of Locke, who confounded abstract and gen- 
eral ideas, the distinctior between these two kinds of idea has been 
very much lost sight of. There are metaphysicians, however, who 
have noticed it. Thus Dugald Stewart : " The words Abstraction and 
Generalization are commonly, but improperly, used as synonymous ; 
and the same inaccuracy is frequently committed in speaking- of 
abstract or general ideas as if the two expressions were convertible. 
A person who had never seen but one. rose might yet have beer 
able to consider its color apart from its other qualities ; and, tlier** 



20 TEE NOTION. 

fore, (to express myself in conformity to common, language) there 
may be such a thing as an idea which is at once abstract and par- 
ticular. After having perceived this quality as belonging to a 
variety of individuals, we may consider it without reference to any 
of them, and thus form the notion of redness or whiteness iu general 
which may be called a general abstract idea." {Elements, Part I, Chap 
IV., § 2, Hamilton's Ed.) Hamilton says : " We can rivet our atten 
tion on some particular mode of a thing, as its smell, its color, its 
figure, its size, etc., and abstract it from the others. This may be 
called Modal Abstraction. The abstraction we have now been con 
sidering is performed on individual objects, and is consequently par- 
ticular [singular]. There is nothing necessarily connected with 
generalization in abstraction ; generalization is indeed dependent on 
abstraction, which it supposes ; but abstraction does not involve 
generalization. I remark this because you will frequently find the 
terms abstract and general applied to notions used as convertible." 
{Metaphysics, Lect. XXXV.) But in his Logic he has allotted no 
separate place to the Abstract Notion, and like all the logicians of 
the school of Kant, he has no other notion than the Concept or the 
General Notion. In consequence of this oversight he has not been able 
to give accurate account of certain peculiarities of thought which he 
has had the shrewdness to notice. As we advance in this treatise we 
Bhall find that we have only to give the abstract notion its proper 
place, to render a clear and scientific account of certain processes of 
thought which the old Logic had overlooked, but which the Kantian 
and Hamiltonian Logic had observed ; and that we can thereby 
remove the hiatus between the Kantian and Aristotelic Logic ; aDd 
rear out of the two a simple and consistent structure. 

22. There is no subject around which there has gath- 
ered a greater amount of confusion of thought and logom- 
achy than the General Notion or Universal. It is oi 
vast moment that we should carefully mark the steps in- 
volved in its formation. 

In order to Generalization two things are pre-supposed. 
The first is, that objects resemble each other, that is, 
possess like qualities. In every department of nature 
there are common properties of form, color, weight, and 
number which enable us to group objects. The second 
circumstance is, that the mind has a tendency to seek out 



SINGULAR AND UNIVERSAL. 2 J 

and discover resemblances. It is induced to do so by 
a native tendency, and it is compelled to do so by 
the circumstances in which it is placed, by the analogies 
which everywhere fall under our notice, and by being 
obliged to put the innumerable particulars that would 
oppress the memory and the understanding into conve- 
nient and comprehensible groups. " To shorten its way 
to knowledge and make each perception more compre- 
hensible, it binds them into bundles." (Locke.) With 
these preliminaries the operation of generalization is 
ready to commence. 

23. First Step. — "We observe a resemblance, more or less 
clearly, among the objects which present themselves. This 
operation begins in early life. Children soon learn to 
distinguish, by their points of agreement, human beings 
from other beings, and the man from the woman, and thei 
child from the adult, and to appreciate practically what 
constitutes a bird, or a cat, or a sheep, or a goat, or a 
horse, provided always that they are in the way of com- 
ing frequently in contact with such animals. All our 
lives we are inclined or compelled to discover agreements 
in the objects or incidents falling under our notice. 
Sometimes the analogies observed are of a practical kind, 
and impart to the man who notices them foresight and 
sagacity ; at other times they are of an intellectual or 
scientific character, and open enlarged views of the con- 
nections of things in the universe ; while others are more 
of a literary or poetical nature, and give rise to com- 
parisons, images, similes and metaphors. 

24. Second Step. — We fix more or less definitely on the 
points of resemblance. The process formerly noticed is 
Comparison ; that now under consideration is a special ex- 
ercise of Abstraction. This abstraction is often of a very 
loose description ; that is, we have not accurately defined 
what the common properties are. We have observed tha 



22 TEE NOTION. 

there is some general resemblance among objects in 
shape, color, or property, and yet if we were to catechize 
ourselves, or if others were to question us, we could not 
tell what it consists in. In other cases, more especially 
in the classifications of natural science, the points of re- 
semblance are precisely fixed and rigidly defined. A 
great deal of the confusion of thought and unsatisfactory 
controversy to be found in the world, originate in men 
never having definitely determined what are the proper- 
ties which combine objects in our common notions. 
Logic promotes clearness of thought by showing that all 
our concepts are formed by common attributes, and by 
insisting on our knowing exactly what those attributes 
are. The common attributes are called technically JVotce 
or Marks by logicians. 

2o» No absolute rule can be laid doAvn as to which of 
the steps now referred to is the prior. In most cases 
there seems to be first a perception of some sort of gen- 
eral likeness, and then the fixing with more or less pre- 
cision on the point or points of resemblance. But there 
are cases in which the abstracting process seems to come 
first. We fix on a quality which is evidently significant, 
and then put all the objects possessing it into a class. It 
is thus that in zoology naturalists fix on the posses- 
sion of a vertebrate column as a characteristic, and in 
botany the springing from one (or two) seed lobes, 
and put together the objects possessing the mark fixed 
on. 

"4(j, Whjchever of these may come first, both are in- 
volved in generalization. But there is more in the process 
than either or than both of these. These are after all 
only preparations for the all-important step. Were the 
operation to stop at this point, there would after all be no 
general notion. For observe that in the comparison we 
have only got individuals, more or fewer, and in the ab 



SINGULAR AND UNIVERSAL. 23 

straction a quality or qualities possessed by individuals. 
The consummating step has yet to be taken. 

27. Third Step. — This is the formation of a class or 
head embracing all objects possessing the common at- 
tribute or attributes. In the first step, the comparison, we 
must have observed or contemplated more or fewer objects 
possessing points of likeness ; still the number was limited. 
In the second step, the abstraction, we have fixed on some 
quality or qualities possessed by them in common. But 
in taking the final step the number of objects becomes in- 
definite : we must have for convenience sake a head 
under which we may place not only the objects we have 
seen, but others we may yet see ; in short, all others possess- 
ing the quality or aggregate of qualities. It is only when 
we take this third step that we have a General Notion or 
a Universal. On seeing only half a dozen buffaloes, W9 
may have been struck with their points of likeness, an 1 
may have been able to determine what these were in our 
minds, specially their shape and mode of motion. But 
feeling it to be useful, we take the farther step and con- 
struct the class ' buffalo,' which must include not only 
these few, but all others of the same form and habit ; not 
only those now living, but all which have lived and shall 
ever live ; not only so, but all conceivable, all possible buf- 
faloes, the wild oxen of fiction and of the ever active 
imagination. 

28. The Universal is thus, in one sense, indefinite ; it 
includes an indefinite number of objects, we know not 
how many, all that possess the Marks. In another sense 
it is definite ; it is defined by the Marks. Sometimes, 
however, the Marks, though supposed to be fixed, are 
very vaguely apprehended by us : thus the great mass of 
mankind know what a buffalo is only by some loose idea 
of its form. We fashion a class called the ' beautiful,' but 
it has been found extremely difficult to determine what 



24 THE NOTION. 

are the common qualities possessed by objects entitled to 
the epithet, and by no others ; and provisionally we can 
only define it as that which raises certain pleasing 
emotions within us. Most classes are ormed in the 
first instance without scientific precision, for mere conve- 
nience sake. Science as it advances seeks to determine 
precisely the Marks of classes, and generally to decide 
what generalizations are worthy of being kept, and what 
are not, and may therefore be allowed to disappear. This 
advance in accuracy sometimes breeds confusion from the 
felt discrepancy between the scientific and popular ar- 
rangements. The class heath was probably formed first 
from the common heather (Calluna vulgaris), which now, 
from the greater precision of the marks, is excluded from 
it. The correct determination of what constitutes ' fish ' 
lias driven out the whale, which is still placed in it in the 
common apprehension. Such general names as value 
and money, have a different signification in political 
economy from what they have in popular language. It 
is one main advantage of the advancement of thinking 
and science, that greater precision and fixedness are im- 
parted to the loose, though often useful, generalizations 
originally fashioned for practical purposes. 

As the aim of every science is to discover Laws, and the 
aim of the science of Logic is to discover the Laws of 
thought, let us enquire what are the 



LAWS OF THOUGHT INVOLVED IN GENERALIZATION 

29» First Law. — The Universal implies Singulars. It 
has been formed out of the singulars. The boy perceives 
an individual crow before he forms any conception of the 
class crow, and it is from the sight or contemplation of a 
number of crows that he forms the general notion. The 



ij AW S IN GENERALIZATION. 26 

Universal notion crow thus throws ns back on the indi- 
viduals entitled to be put under it. It is the same with 
every other common notion. The Universal is neither 
less nor more than individuals viewed as possessing cer- 
tain attributes in common. 

SO. Second Law. — When the Singulars are Eeal, the 
Universal is also Real. We perceive a number of bushes 
before us, and observing that they agree in having tne same 
shape and structure and in having spines, we put them 
under one head, thorn. What is now affirmed is, that 
if the individual bushes exist, so also does the tribe. The 
tribe has a reality in the real bushes, and in the common 
attributes possessed by them. True, if the singulars are 
ideal, so may also be the genus. If there be no such beings 
as ghosts and. fairies, then the class cannot be said to have a 
reality. The question of the reality of the class is thus to 
be determined by inquiring whether the individuals, and 
the attributes involved in the classification, have a rea. 
existence. 

31. Third Laio. — The "Universal has a reality in the 
Singulars, and in the Common Properties possessed by 
them, but no Independent Existence. We are not to sup- 
pose that the species ' rose ' has the same kind of existence 
as the individual rose : or that ' the beautiful ' has the 
same sort of reality as a lovely star or a lovely woman : 
or that ' the good ' exists as the good God does. The 
Universal, say rose, beautiful, good, has an existence only 
in the single roses, and in the objects which are beautiful 
and good, and in the common qualities combining them, 
If the Singulars were to cease, the Universal would also 
cea.e. Give us individuals possessing a common attri- 
bute, and we may form a common notion out of them. 
Let the individuals have an actual existence, and the 
notion will have the same, always in the objects and the 
marks by which they are grouped. In this sense not 



26 THE NOTION. 

only what are called natural classes such as Ranuncu- 
lacese, Rosacea, Mollusca, but even such generalizations 
as beautiful, virtuous, clear, high, low, level, united, scat- 
tered, have a reality in the common properties of the 
things joined under these heads. "When we say that this 
rose is beautiful, we mean that it is an object possessing 
the attributes which bind in one notion the objects en- 
titled to be called beautiful. 



EXTENSION AND COMPEEHENSION OP GENERAL 
NOTIONS. 

32. According to the account now given, every General 
Notion embraces two things : it embraces objects, and it 
embraces attributes. Thus the notion vertebrata com- 
prises objects, viz. : all animals possessing the common 
property ; and it also implies an attribute, the possession 
by all the animals of a vertebrate column. The former of 
these is called by logicians the Extension, and the latter 
the Comprehension or Intension of a notion. The no- 
tion Rational Being is said to have Extension, inasmuch 
as it embraces all objects possessing reason ; and Com- 
prehension, inasmuch as all these possess the attribute of 
reason. The Extension of a Notion is reached specially 
by generalization as above described ; the Compre- 
hension specially by abstraction, that is, by fixing on 
marks. It is clear that some notions have greater Exten- 
sion than others : thus man has greater Extension than 
Frenchman ; that is, it embraces a greater number of 
beings. Some Notions, again, have greater Comprehension 
than others : thus Frenchman has greater Comprehension 
than man, for he has all the attributes found in mankind 
generally, and some peculiar to those who dwell in France. 
It is evident that the greater the Extension of a term. 



EXTENSION AND COMPREHENSION. 27 

that is, the number of objects denoted by it, it has the 
less Comprehension, that is, fewer attributes common to 
the objects ; and vice versa, the more the Comprehension 
of a term, that is, the number of marks possessed by all 
the objects, the less its Extension, that is, the fewer are 
the objects possessing the whole of them. 

S3. The distinction between the Extension and Comprehension 
of a Notion, though stated earlier, was introduced formally into 
Logic in La Logique ou VArt de Penser, by Arnauld and Nicole 
(1662 A. c). It is found in a number of logical treatises published in 
the end of the 17th and beginning of the 18th century. It has been 
revived by Sir W. Hamilton. It should be remarked that it applies, 
only with a modification of its meaning, to Abstract Notions (§10) 



HIGHEK AND LOWEE GENEEALIZATIONS. 

34* The objects embraced in a Common Term are 
commonly combined, not by the possession of one attri- 
bute but of several, sometimes an indefinite number. In 
all such cases we can form higher and higher generaliza- 
tions. Take the class Dog, it is evident that it includes 
an aggregate of attributes, so many indeed that we can- 
not specify them all. Now we may fix on any one of 
these, and put all the objects possessing it into a group : 
thus we may fix on the quality of eating flesh, and form 
the general notion Carnivora. Looking again at Carniv- 
ora, we may fix on the possession of a backbone and form 
the class Vertebrata, and in Vertebrata we may single out 
the property of organization and form the notion Organ- 
ized Being. The following table may illustrate the pro- 
cess : 

Being. 

Substance. 

Matter. 

Organized Matt* j 

Animal. 



28 THE NOTION. 

Vertebrata. 
Mammal. 

Carnivora. 
Dog. 
Terrier. 
Snap. 
35 '. It is desirable to have a nomenclature to express 
the relation of the classes in this scale, and logicians have 
supplied us with such. Thus suppose we fix on any class 
possessing a group or aggregate of properties such as 
Dog, the logicians would call this Species ; and then the 
class above it, Carnivora, would be called Genus. But 
as we may often have occasion to speak of the relation of 
a greater number of classes we need other phrases, and 
logicians use Proximum Genus to express the class next 
above the species, and Subaltern Species the class next 
below the species. Thus fixing on Dog as the species, 
Carnivora might be the Proximum Genus, and Mammal 
the Genus ; while Terrier would be the Subaltern Spe- 
cies. The highest genus which we can form is the Sum- 
mum Genus ; and the lowest species which Ave can form, 
the Infima Species — a point which, however, we can never 
absolutely fix. If we take all things, the Sum mum Genus 
is Being ; if we take merely an order of things, the Sum- 
mum Genus is the highest in that order ; thus Plant is 
the Suminum Genus in Botany, and Discursive Thought 
in Logic. It is evident that the Sumruum Genus can 
have no species above it, and that the Infima Sjoecies has 
only individuals and no species below it. Looking to 
the Table we see that the individual has the greatest 
Comprehension, it has an aggregate of attributes which 
nobody could specify ; and the least Extension, for it has 
only one object. On the other hand, the Summum Genus 
has the greatest Extension, for it includes all objects ; and 
the least Intension, for it comprises only one attribute. 
Between these two extremes, the Extension rises as we 



HIGHER AND LOWER GENERALIZATIONS. 29 

ascend the scale, while the Comprehension diminishes ; 
and as we descend, the Extension is lessened while the 
Comprehension is increased. All this follows from the 
nature of Generalization and the General Notion. 

30. These remarks as to relative Extension and Inten- 
sion presuppose that £he same objects are generalized 
throughout. But mankind form classes among the in- 
numerable objects which present themselves as conve- 
aience induces and necessity requires ; and it is only in a 
few sciences that we have such a regular subordination 
as in the above table. In such general notions as plant, 
planet, money, revolution, virtue, we have no relation 
implied except that they may be all placed under some 
one high genus such as Being. In comparing such no- 
tions we can say nothing as to their relative Extension or 
Comprehension. 

37. A notion is said to be Subordinate to another no- 
tion when it is included in the Extension of that other : 
thus 'carnivorous' is Subordinate to ' mammal.' Notions 
are said to be Co-ordinate when they are species imme- 
diately under the same genus : thus mammals, birds, 
fishes, reptiles, are co-ordinate notions under the genus 
vertebrate. Notions are said (by Leibnitz) to be Commu- 
nicant when they overlap each other, as e. g. ' poetical 
writers' and 'writers of tales,' there being some writers of 
tales who are poetical writers and others who write in prose. 



TEE SINGULAR CONCRETE, THE ABSTRACT, AND 
UNIVERSAL NOTION. 

38. All notions we have seen are either Concrete or 
Abstract. All notions w T e have farther seen are either 
Singular or Universal. These divisions are made accord- 
ing to different principles or marks. The former is a 



30 THE NOTION. 

division in respect of attributes or notce, that is, marks ; 
the mental process involved is abstraction ; and it pro- 
ceeds according to the comprehension of the notions 
The latter is a division in respect of individuals and 
classes ; the mental process involved is generalization ; 
and it takes place according to the extension of the no- 
tions. These are cross divisions ; let us combine them. 
Our first idea might be that we ought to have four kinds 
of notions. But it so happens, that all notions which are 
Singular are also Concrete, that is, have an aggregate of 
attributes ; and abstraction is in the Universal as well as 
the Abstract Notion. We have, in consequence, a three- 
fold division : 

1st. The Singular Concrete, as Bucephalus, This 
Animal. 

2d. The Abstract, as Swiftness, Life. 

3d. The Universal, as Swift, Animal. 

30, The things apprehended in the first may be called 
Percepts, in the second Abstracts, in the third Concepts. 
It will be found that all the notions which the mind of 
man can form, are either Percepts, Abstracts, or Concepts. 

40. The Singular Concrete Notion, or Percept. — This is 
the notion with which the mind starts, and from which 
the two other kinds are derived. It is of objects as 
they present themselves ; and these are known as sin- 
gle, but with a number of qualities. As our observation 
increases we come to know a greater number of indi- 
vidual objects ; and we know each possessing a greater 
number and variety of qualities, as it were more and more 
in the concrete. This piece of iron : we may know it 
first as a mere lump of matter, with a certain shape and 
color ; then we know it as hard ; as capable of being 
melted by heat ; as capable of being rusted, that is, com- 
bined with oxygen ; as capable of being formed into 
certain useful utensils, and as possessing special mag- 



PRECEPTS, ABSTRACTS, CONCEPTS. 31 

uetic powers. As we thus add one property after an* 
other to objects, we are constrained at last to acknow- 
ledge that we cannot know all the attributes possessed 
by any one thing. Who can tell all the qualities pos- 
sessed by any one metal, plant, or animal ? 

41. The Abstract Notion, or the Abstract. — This is pro- 
bably the second kind of notion formed by the mind in 
the order of things. On a concrete object coming before 
us, we can contemplate a part of it as a part, or an attri- 
bute of it : thus having seen Bucephalus we can think of 
his swiftness. Having an idea of an animal, we can con- 
template its life. These Abstract Notions, like all other 
notions, may be expressed in one word or in several. 
Thus ' swiftness ' and ' life ' are abstracts designated by 
one word. Quite as frequently the notion is embraced in 
a number of words ; and it is of importance that we be 
able to fix on the one Abstract in the midst of the multi- 
plicity of phrases. When we say, " to repeat a hundred 
lines on once hearing them can be done only by a few," the 
words in Italics express only one abstract idea. " It is a 
true saying, and worthy of all acceptation, that Jesus Christ 
came into the world to save sinners ; " here " Jesus 
Christ coming into the world to save sinners " is one no- 
tion, and that abstract. Logic serves a most important 
purpose when it leads us to detect the Abstract No- 
tion wherever it is found ; to perceive exactly what sort 
of existence it has ; ever to go back from the abstract 
quality to the concrete objects ; and to acknowledge in the 
abstract no other reality than that which is to be found 
in the objects. 

42. The Universal Notion or Concept. — To this Notion, 
or rather thing conceived, I am inclined to restrict the 
phrase 'Concept' (Begriff in German). The derivation 
of the word (from con and capio) requires that it should 
be applied to those notions, in which we seize on a 



yz TEE NOTION. 

number of things and bring them into a unity of 
thought. The Concept thus understood always em- 
braces an indefinite number of objects, all the objects, real 
or potential, possessing the attribute or attributes which 
we have fixed on as the ground of the generalization. 
The Common Term, which is the Concept expressed in 
language, can be applied to any one of these objects. 

43. A distinction of some importance may be drawn 
between two kinds of Universals — between what I venture 
to call the Generalized or (simply) General Abstract, 
and the Generalized or (simply) General Concrete. 

4:4. The General Abstract. — In this we have only some 
one quality, or with qualities involved in it, to constitute 
the marks of the notion. Thus 'just' is evidently a 
common term — it embraces all intelligent beings and acts 
possessing the quality of ' justness.' But it denotes only 
one attribute, that designated by the term. Of the same 
description are such classes, as faithful, true, frank, gen- 
erous, hard, soft, tough, elastic, indeed all adjectives. To 
such I would apply the scholastic phrase, connotative ; 
they denote an attribute and they connote objects. 

4o. The General Concrete. — In this, a number of the 
aggregate of qualities to be found in the singular objects, 
go up into the General Notion. Thus we have in every 
individual animal a variety of properties which no one 
can number. Not only so, we have in the general term 
' animal' a collection of attributes the whole of which no 
wise naturalist will venture to specify. Of the same 
character are man, mineral, vegetable, metal, horse, dog, 
rose, lily ; no one should profess to be able to fix on all the 
attributes which are found conjoined in every individual 
of the class. It is not difficult to perceive the difference 
between these two kinds of notions. Both are Universal, 
for they include an indefinite number of objects. But in 
the one the attributes are specified ; they are such as faith- 



THE GENERAL ABSTRACT AND CONCRETE. 33 

fulness, generosity, hardness. In the other they are not 
denned ; they consist of an aggregate of qualities found 
in all the objects. 

4:0. It should be specially observed, that it is classes 
of this latter description which admit of higher and ever 
higher generalizations. The boy observes that certain of 
the animals with which he is familiar resemble each other, 
and he groups them into such convenient classes as dogs, 
horses, cows. Then, as he is introduced to the elements 
of science, he is taught that all these have certain 
agreements, and that they may be placed in the class 
quadruped, or mammal. Comparing this with other 
tribes, such as birds, fishes, reptiles, he finds them all in 
possession of a back-bone, and he calls them vertebrata. 
In this way we may mount upward till we come to Being, 
which denotes existence without qualit} 7 . Let it be ob- 
served that all this proceeds on the circumstance, that as 
individuals possess an aggregate of qualities, so also may 
classes of objects. When we come to Being we have 
risen above the General Concrete to the General Abstract 
Notion. 

47. The circumstance that there are Concrete General 
Notions has cost logicians a great deal of trouble, and 
often landed them in inextricable confusion. It was sup- 
posed by many of them that a genus or a species was con- 
stituted by a certain number of knowable attributes. The 
schoolmen were ever seeking after a species which would 
constitute the whole essence of its objects. And this leads 
me to remark that we believe the schoolmen would not have 
applied the phrase Species to any class except one with 
an aggregate of properties. But in natural classes we 
are not able to point out all the qualities possessed in 
common by the objects. No man of science will venture 
to say that he knows all the qualities which go to consti- 
tute the essence of metal, or plant, or man. 



34 THE NOTION 

" Men define a man 
The ci sature who stands frontward to the stars, 
The creature who looks inward to himself, 
The tool-wright, laughing creature. 'Tis enough ; 
We'll say the inconsequent creature man, 
For that's his specialty. What creature else 
Conceives the circle and then walks the square ? " 

The circumstance that every object, and most classes of 
objects, possess a number, apparently an infinite number 
of properties, lands the logician in perplexities and 
threatens to destroy the symmetry of his system. And 
were the various properties of things loose and uncon- 
nected, it would be impossible to reduce the Concrete 
Generals to anything like order. As an infinitely worse 
consequence, it would be found impossible to arrange 
natural objects iuto natural classes. For the number of 
qualities in all objects material and mental being innu- 
merable, we might fix with equal propriety on any one as 
the ground of the arrangement, and different persons 
would fix on different qualities, and there could be no 
agreement among those investigating the kingdoms of 
nature, or rather we should not be able to speak of the 
kingdoms of nature. But the Grod who made all things 
has, happily for our understandings and our practical con- 
venience, instituted an order among the separate qualities 
of objects, so that it is possible to arrange them into 
orders which have such Marks as enable us to fit them 
into our natural systems. This will be explained in a 
coming section, when we consider the aids to generaliza- 
tion in the works of nature. 



MIXED NOTIONS. 

4S» We hold that all notions can be referred to one or 
other of these three heads. At the same time the three 



MIXED NOTIONS 35 

may be mixed up with each other in a number of ways. 
Thus there is the Singular Classified, as ' that statesman,' 
' that orator,' ' that general,' c that philanthropist.' These 
notions are all singular, but the object is put into a class 
Such singular terms are to be distinguished from Singu- 
lars Proper, or proper names, such as William Pitt, Ed- 
mund Burke, George Washington, William Wilberforce. 
A.gain, there is the Singular Collective, or Collective 
Term, which is in itself Singular, but embraces objects 
put in a class : thus the ' Forty-second Regiment ; is 
a Singular Notion, but it applies only to soldiers who are 
classified ; ' House of Representatives ' cannot be applied 
to each of the members, but each of the members is a 
representative of the people. There is also the Singular 
xlbstracted : as when we say Wellington was the con- 
queror at Waterloo, the term " Conqueror at Waterloo " 
is Singular, is one thing, but that thing viewed under an 
abstracted aspect. 

40. It is to be specially noticed that very many Terms 
are used both as Abstracts and Concepts. The tendency 
always is, when we have seized on an important quality, 
especially when we have coined a word to express it, to 
make it the bond of objects, which we join in a class. 
Thus, having noticed that certain persons possess a qual- 
ity which we call ' learning,' we form a class called 
' learned,' to embrace all who possess the attribute. Quite 
as frequently we constitute a class by the possession of a 
number of attributes, known or unknown, and we join 
ah these in one by giving them a name. Thus, without 
settling what living beings possess in common, we desig- 
nate what they agree in by the abstract phrase ' life.' It 
is thus that we have ' generous ' to connote the class, and 
' generosity ' to denote the quality. In these cases the 
abstracts and concepts are designated by somewhat dif- 
ferent though related words. But in raanv cases the 



36 THE NOTION. 

same term may denote both the abstract and general 
notions. Thus ' virtue ' is primarily an abstract term ; 
we have formed it by abstracting a certain quality of in- 
telligent and moral beings. But then the quality has 
various forms as it appears in different individuals, and 
at different times, and we classify the diversities and 
speak of different virtues, such as justice, and temperance, 
and benevolence, thus making the phrase general. Fine 
Arts is an abstract term, but it may become a common 
term with painting, architecture, and sculpture, as sub- 
classes. Pain and pleasure are in themselves Abstracts, 
but may embrace under them various kinds of sensations, 
as corporeal and mental enjoyment, and suffering of 
body, and anguish of spirit. In many cases it is of 
great importance to determine as to a phrase which may 
be both abstract and general, in which of the senses it is 
employed in a given passage or discussion. Such terms 
as ' substance,' ' quality,' and ' mode,' may be one or 
other ; and in every speculative investigation we should 
settle in which of the senses we are employing it. Sub- 
stance is primarily an Abstract, standing for that which 
abideth in objects material or mental. It stands for a 
Concept when we speak of two substances, mind and body. 
50. Students of logic should notice that there is one 
class of Abstract Notions which always tend to become 
general. Verbs are primarily abstracts expressing ob- 
jects, not in the concrete, but as being, doing, and suf- 
fering. But when they are used in propositions they may 
become general. When we say that " man speaks," the 
sentence is primarily attributive ; it means that man has 
the power of speaking. But the term ' speaks ' may also 
be interpreted as universal ; it may mean that man is in 
the class of speaking creatures. We shall see, as we ad- 
7ance, that when a verb is used as a middle term in 
reasoning, it is alwavs to be understood as a universal. 



MIXED NOTION'S. 37 

Thus, when we argue that since men speak, and gorillas 
do not speak, therefore gorillas are not men, we must, in 
order to the legitimacy of the reasoning, understand 
c speak ' as denoting all speaking creatures. 

51. We form notions of various complexity by accre- 
tion and agglomeration. These are called Mixed Modes 
by Locke. Thus we speak of ' a procession,' implying 
persons, and a train, and time, and succession. We talk 
of ' a triumph ' implying a battle and a victory, and a 
display. We join abstracts to abstracts ; we speak and 
write of ' the triumph of excellence,' of ' the defeat of wick- 
edness,' of ' the reward of righteousness ' and ' the pun- 
ishment of evil,' of ' the beauty of natural scenery,' of ' the 
hopefulness of spring,' of ' the gloominess of winter,' of 
'the madness of passion,' ' the terrors of despair.' We join 
general with abstract notions. Thus we have the abstract 
idea ' wickedness,' and we have the general notions 
' human,' and ' demoniac,' and we talk of ' human wick- 
edness ' and ' demoniac wickedness.' We have expe- 
perienced ' joy ' and ' sorrow,' and we know what ' eleva- 
tion ' is and what ' depression ' is, and we speak of ' the 
elevation of joy ' and 'the depression of sorrow.' 

52. But whatever be the genesis of our notions, in the 
end they come to be either Percepts, or Abstracts, or 
Concepts. To avoid confusion of thought and misappli- 
cation of terms, it is of moment that we should be able 
to say as to every given notion, under which of these 
heads we are to place it. When we say " Shakespeare's 
Plays are the best in the English language," the one no- 
tion " Shakespeare's Plays " is Singular Concrete (Collec- 
tive), and the other "the best in the English language," 
an Abstract. When we say " Logic is the science of the 
Laws of Discursive Thought," the two terms "Logic" 
and " the science of the Laws of Discursive Thought," are 
both Abstracts. When we say "the hearts of sufferers 



38 TEE NOTION. 

can be won only by love," the two notions " hearts oi 
sufferers " and " can be won only by love" are both 
Universal. 



PEIVATIYE NOTIONS. 

53. We have seen that in Universals, objects are bound 
into one by the possession of Marks. But we may also 
unite objects by the absence of Marks. Thus we say that 
all quadrupeds are vertebrates ; and we say of mollusca, 
that they are invertebrate. The former of these notions is 
called Positive, and the latter Privative. Logicians have 
remarked that a Positive and Privative Term divide 
among them the universe of being, that is, all objects 
must either be vertebrate or invertebrate. But when in- 
terpreted properly, this means simply that each object 
must either possess or not possess a given attribute. It 
does not imply that the non-possession of that attribute 
is a proper mark by which to join objects. There would 
be no propriety in putting all objects which do not pos- 
sess a back-bone, say thought, the soul, probity, dress, 
planet, into the class invertebrata — which should be ap- 
plied only to those portions of the genus animal which 
we wish to distinguish from vertebrates. It should be 
remarked that some seemingly privative phrases really 
imply a positive Mark : thus the phrase ' immortal ' im- 
plies not merely that the object does not die, but that it 
lives forever ; and the term ' infinite ' may be held as 
meaning more than merely the absence of bounds, it in- 
volves the occupation of all space and all time. 



LOGICAL DIVISION. 39 

CONTKAEY AND CONTRADICTORY NOTIONS. 

54. Positive and Privative Terms are said to be Con- 
tradictory ; that is, they are such that we cannot concvjive 
them as applied to the same object at the same time, such 
as existent and non-existent, organic and inorganic. 
Contrary Terms, called by some Id compatible, are such 
as might be conceivably applied to the same object, but 
cannot, in fact, be so applied, such as good and bad, light 
and darkness, cold and hot. 



KELATIVE NOTIONS. 

55. These are derived, not from a quality in one ob- 
ject, but from the relation of one thing to another. When 
we speak of the objects under this relation, they are said 
to be Correlative. Thus we have sovereign and subject, 
parents and children, husband and wife, master and ser- 
vant. The one of these implies the other. The;y are 
connected by the ground of the relation {fundamentum 
relationis). The phrases themselves are Universals (Gen- 
eral Abstracts) ; the relation, say that of sovereignty and 
subjection, is abstract ; for relatio non est per se reale, sed 
per suum fundamentum. 



LOGICAL DIVISION. 

50. In generification, that is, in the formation of 
common notions, we rise from singulars to classes, and 
from lower classes to higher. But after the classes have 
been fashioned by ourselves or others, we may reverse 
the process and descend from higher classes to lower 



tU THE NOTION. 

This operation is called Logical Division, which may be 
defined, as the process by which we spread out a genus 
into its co-ordinate species. It is to be distinguished 
from Partition, which consists in separating an individual 
object into its parts ; as when we sunder a plant into stems, 
roots, and branches. Logical Division takes up a common 
notion, such as plant, and spreads it out into acotyledons, 
monocotyledons, and dicotyledons. To every such sub- 
class the name of the higher class may be applied ; 
thus we speak of plants, monocotyledonous, and dicotyle- 
donous, and in the same science of Geum urbanum and 
Gfeum rivale. It is evident that Division proceeds speci- 
ally according to the Extension of a notion ; and it in- 
volves Comprehension only so far as Extension implies 
Comprehension. The rules are : 

o7. First Rule. — We must proceed according to a 
Mark or Marks added, and according to the same Mart 
or Marks throughout. We have seen that in the ascend- 
ing process of generification, Ave leave out marks ; thus 
in ascending from dog to camivora, we leave out every 
property of the dog except that of eating flesh. In the 
descending process of division we add marks. Thus in 
dividing plants, we add the property of growth by seed- 
lobes, and put those growing from one seed-lobe under 
one head, and those growing from two, under another. 
Discursive Thought is divided into the Notion, Judgment, 
and Eeasoning, according as we exercise thought in ap- 
prehending, in comparing the things apprehended di- 
rectly, or comparing them by means of a middle term. 
As in our divisions we proceed on a principle, so that 
principle should always be clearly understood and very 
commonly be enunciated. What should be the Marks 
fixed on must be determined by the nature of the objects, 
and the scientific or practical end we have in view at the 
time. Here Logic can be of little use to us ; but then it 



LOGICAL DIVISION. 41 

serves an important purpose by insisting that there must 
be Marks. It does more : it requires that we proceed 
throughout on the same Marks. In dividing mankind, 
we may proceed on various principles : as on the princi- 
ple of race, into Caucasian, Malay, Mongols, Negro ; on 
the principle of enlightenment, into savages, uncivilized 
and civilized ; of religion, into Christians, Mahometans, 
Pagans. But it would be wrong to flit from one of these 
to another, and divide mankind into Christians, Mahom- 
etans, and savages ; or into Europeans, Americans, Pa- 
gans and Mahometans. The logician would err were he 
to divide discursive thought into the term, the proposition, 
and argument ; for in the first he would be proceeding on 
the principle of language ; in the second, on that of 
thought. Arrangements violating this rule are called 
' cross-divisions.' " It is a useful practical rule, whenever 
you find a discussion of any kind very perplexing and 
seemingly confused, to examine whether some cross- 
division has not crept in." (Whately). 

58. Second Rule. — The specie^ must make up the 
genus, or, as it is otherwise expressed, the dividing mem- 
bers (membra dividentia) must make up the whole. This 
rule would be violated were we to divide vertebrate ani- 
mals into quadrupeds, birds, fishes, and reptiles ; for there 
are animals — man, for instance — included in vertebrata, 
but not in the division. We shall see, in treating of Judg- 
ments, that Immediate Inferences can be drawn on the 
principle of division ; but this can be done only on the 
assurance that the division is complete. There is often a 
fallacy lurking in imperfect divisions. Thus the Eleatics 
argued that there could not be such a thing as motion, 
for that the motion must either be in the place where it 
is, or in a place where it is not, neither of which is pos- 
sible ; whereas there is a third supposition that it may 
have been from the place where it was, to the place wherf 



42 THE NOTION. 

it now is. Another sophism proceeds on the same mis- 
take. It is argued that academical honors are useless, 
inasmuch as they are not needed by those who have a 
taste for study, and that they have no effect on the idle, 
and such as are indifferent to mental improvement. Here 
it is tacitly assumed that all students must belong either 
to the diligent class or the idle class ; whereas there 
may be a large intermediate class, not altogether hope 
lessly idle on the one hand, nor with confirmed habits oi 
application on the other, and these may be influenced by 
academical distinctions. 

5i). Third Rule. — The dividing members must exclude 
one another. This rule would be violated were we to 
divide lines into straight, curved, circular, and elliptical, or 
notions into singular, concrete, abstract, and universal — 
for concrete notions may be universal. He who neglects 
to attend to the rule, will offend every person of correct 
judgment, and confuse the minds of those who do not 
see the fault of the division. The preacher violated it 
when he proposed proving a particular doctrine from 
reason, and from revelation, and the testimony of Paul ; 
his division should have been from reason and from rev- 
elation, and under the latter, he might have said, espe- 
cially from the testimony of St. Paul. The barrister trans- 
gressed it when he talked of establishing his point by 
moral law, by the law of the land, by Act of Parliament 
and precedent ; for Acts of Parliament and precedents 
are included under the law of the land. The Chinese are 
said to furnish a ludicrous example of this error in their 
division of the race into first Chinese, then men, and then 
women. The error arises commonly from introducing 
subordinate species and not adhering to co-ordinate 
species. It will often happen that a division contraven- 
ing any one of these rules will also violate all the others. 
Thus a librarian who would arrange his volumes as books 



LOGICAL DIVISION. 43 

of prose, poetry, morals and religion, as proceeding on no 
principle, would never be able to make up tlie whole, and 
would find his divisions running into inextricable con 
fusion. 

GO,- Fourth Bide. — There should be a due subordina- 
tion of classes — Divisio non faciat solium. The contents 
of elaborate treatises are commonly distributed into 
Boohs, Chapters, and Sections. We should never be able 
to arrange the vegetable kingdom if we proceeded to dis- 
tribute plants as they cast up into roses, oaks, lilies, 
lichens ; nor the animal kingdom if we began to divide 
them into horses, dogs, leopards and lions. Naturalists 
fix on a regularly ascending or descending series of 
divisions and sub-divisions ; thus Agassiz arranges the 
animal kingdom into Branches or Types, Classes, Orders, 
Families, Genera, Species. 

01. These rules are of value in the sciences, especially 
those which are concerned with classification, such as 
Botany and Zoology. True, they do not tell us how we 
are to arrange the organic world, for this must be done 
by a careful observation and induction of the facts ; but 
they lay down certain stringent laws of thought which 
must be attended to in the classifications formed. They 
may also be of great service in the construction of essays, 
papers, sermons, and discourses of every kind. It is not 
necessary in all cases to announce the division. Some 
people have argued that such an announcement must 
make the composition stiff and formal, and is apt to 
damp the curiosity of the reader or hearer who ought to 
be kept awake by a desire to know what is coming. On 
the other hand, it is argued that when our end is not 
merely to please or tickle the fancy, but to impart in- 
struction, it is of importance to announce the divisions 
an i subdivisions, which will be found greatly to aid the 
memory and comprehension. The question of whether 



44 THE NOTION. 

we should or should not lay down a formal division is tc 
be decided by the end we have in view, whether it is sim- 
ply to amuse or interest for the time, or to convey impor- 
tant truth which we expect to be recalled and pondered. 



ANALYSIS AMD SYNTHESIS. 

62. Analysis (from dvaXvo), I unloose), is that process 
in which we separate in thought, a concrete object or a 
complex abstract notion into its parts or qualities. Analy- 
sis is always performed by means of Abstraction, but the 
two differ. In Abstraction we mentally separate any 
quality ; in Analysis we spread out the qualities which 
make up the whole. It is seldom we can unfold all the 
properties of a concrete object, and not always that we can 
fix on all those of a complicated notion. There are times, 
however, when we can bring' out to view the attributes 
involved in an abstract which we have fashioned. Thus 
we analyze discursive thought into thought as directed to 
objects whatever they be, and thought as directed to special 
classes of objects : and the former we analyze into Simple 
Apprehension, Judgment, and Reasoning. We thus see 
that Analysis is not the same as Division. In Division 
we take a class and distribute it into sub-classes ; in 
Analysis we take a concrete object, or more frequently a 
comprehensive abstract, and spread out its qualities. It 
may happen that where an abstract term is also a com- 
mon term, division and analysis coincide. Thus, as 
' Discursive Thought,' and as ' Notions,' ' Judgments,' 
and ' Reasoning,' are at one and the same time Abstracts 
and Concepts, it is of little moment whether we call the 
distribution of them a division or an analysis — whether 
ive say that we divide or that we analyze the notion into 
percepts, abstracts, and concepts. 



ANALYSIS AND SYNTHESIS. 45 

03. Having found the parts by Analysis, we may join 
the parts to show that they niake up the whole by a pro- 
cess which is called Synthesis (from ovvrldrjiu, I place 
together). When we can prove that the parts by their 
junction constitute the whole, the synthesis is a confirma- 
ation of the accuracy of the previous analysis. It is clear 
that in the study of a new or hitherto unexplored subject, 
we must begin with analysis. But after we have made a 
successful analysis, we may then advantageously employ 
synthesis in corroborating the previous analysis, and the 
synthetic method in expounding the science which treats 
of the objects. Thus in chemistry, having shown what 
the elements of bodies are, we may then take up these 
elements one by one, and show how we can explain by 
them the composition of all bodies. Thus in Logic, hav- 
ing ascertained by analysis that thinking consists in Simple 
Apprehension, Judgment, and Reasoning, we then con- 
sider each of these, and show how they together consti- 
tute the discursive operations of the mind. Whately has 
imparted a great interest to his Elements of Logic by in- 
troducing us to the subject by an analysis of the reason- 
ing process, and then proceeding to develop the science 
in the synthetic method. 

64. Analysis and Synthesis used to occupy a much more important 
place in Logical treatises than they now do. They were represented 
as the main instruments in the investigation of nature. It was, in 
fact, very much by mental analysis and synthesis that the philoso- 
phers of ancient Greece and Rome and the medieval logicians and 
theologians proceeded in their physical speculations. The instru- 
ment is now seen to be Induction, and Deduction joined with it in 
certain walks of inquiry. But it can be shown that analysis is an 
important element in Induction Phenomena falling under the 
senses or our observing faculties are always concrete or complex 
and we must so far separate the things which are joined together 
before we caii reduce them to a law, or even observe them. Hence 
Bacon says, we must begin Induction by the "necessary rejections 
or exclusions ; " and Whewell says by " the Decomposition of Facts ' 



*6 THE NOTION. 

It can be shown also that Synthesis may act an important part in 
Deduction. But these questions carry us into Inductive Logic. 



LOGICAL DEFINITION. 

(to. By definition (opLOfiog) is meant in the most gen- 
eral sense " a description which manifests the nature of 
the thing defined." Logical Definition is to be distin- 
guished from mere verbal explanation : as when a child 
does not understand what is meant by perspicuous, and 
you say it means clear ; or when you say that salubrious 
means tending to produce health. It is the province of a 
dictionary to give the explanation of words. But in de- 
finition we must manifest the nature of the thing defined. 

6'6» We can logically define only those notions in 
which there has been a process of discursive thought ; 
that is, abstract or general notions. We cannot, pro- 
perly speaking, define a singular notion, for we cannot 
manifest its nature by bringing to view all its attributes, 
the attributes being innumerable. All we can do is to 
give some marks of the individual, technically called a 
description, sufficient to detect the object and distinguish 
it from others. We have such a description in the " Hue 
and Cry" sent after a criminal, " five feet eight, light 
hair, blue eyes, a scar on the right cheek." We have 
such descriptions, sufficient to enable us to recognize them, 
of towns, rivers and mountains, in our traveller's guide- 
books. 

07. It has been remarked by many philosophers tha! 
there are some notions which cannot be defined. It wil] 
be found that these are abstracts : they are qualities which 
cannot be resolved into anything simpler, such as sweet- 
ness, sourness, pleasure, pain. We can give no idea of 
them to one who does not know already what they are : 



JUOGIGAL DEFINITION. 47 

all that we can do in explaining our meaning is to appeal 
to our experience of them. But while we cannot define 
them so as to manifest the nature of the thing, we can 
make a great many affirmations and denials regarding 
them. Thus we can say that such a sour taste is pro- 
duced by vinegar ; that a purple color proceeds from the 
union of yellow and blue rays. Much information can 
often be given by specifying the objects in which the 
quality is to be found : thus we can say that pleasure 
and pain are affections of beings endowed with sensation. 
We car always make an indefinite number of negative 
statements regarding these simple ideas, to face misap 
prehensions or misrepresentations, as that pleasure does 
not consist in the mere possession of wealth, or the means 
of sensual gratification. But there are cases in which we 
can give a definition of an Abstract Notion ; being com- 
plex we can analyze it into its constituents. Thus we can 
define Discursive Thought as an exercise of mindinwmich 
we proceed from something given or granted, to some- 
thing else founded on it. 

68. It is disputed among metaphysicians whether such ideas as 
those of Extension, Power, Moral Good, are to be put under the 
same head as those of pleasure and pain ; that is, under the head of 
original ideas, revealed to us by the senses or primitive perceptions. 
When asked to define virtue, or moral good, we can only say virtue 
is virtue, good is good. But then we can make an indefinite num- 
ber of negative propositions regarding them : thus we say that vir- 
tue or good does not consist in mere happiness ; and that the rela- 
tion of cause and effect does not consist in invariable antecedence 
and consequence. 

00> We should always be able to define a General 
Notion. We have seen that objects are brought together 
mto a common notion by means of the possession of a 
common attribute. Now we can bring out this attribute 
in definition, and in doing so, we indicate the bounds of 
the common notion, and thus what it is as distinguished 



48 THE NOTION. 

from other things. It is evident that definition proceeds 
specially according to the Comprehension of a notion. 

70. First Rule. — We must bring out a distinguishing 
attribute of the notion defined. When this is done there 
is always a true definition. When this is not done there 
is no proper definition. When we say man is a rational 
being, we have given a sufficient definition ; for rationality 
is a characteristic quality not found in inanimate nature, 
or in the brute creatures. When we say Logic is the 
science of the discursive laws of thought, we have brought 
out a distinctive mark, distinguishing the science from all 
sciences with which it might be confounded, such as 
Ethics and MetajDhysics. As to what is a distinguishing 
property of a notion, this must be determined not by 
Logic, but the sciences which deal with the objects. But 
Logic insists on our fixing on such a property. Herein is 
the person trained to logical habits distinguished from 
others. How often do we find the uneducated man 
struggling to give expression to what he knows in a loose 
way, and failing. You ask him what Logic is, and he 
answers a branch taught in our colleges ; what Arithme- 
tic, and he says a branch taught in our schools ; what 
Language, and he says a means of expression — as if there 
were not other branches taught in colleges and schools, 
and as if there were not other ways of expressing thought. 
The person disciplined in Logic knows that in giving a 
definition he must fix on a distinguishing attribute, and 
he seeks for it and is not satisfied till he finds it. 

7 1, And here it is of importance to remark how it is 
that what we have called the General Concrete Notion is 
defined. It is evident that we may not be able to bring 
out all the attributes common to the notion, for we may 
not know what they are. It is enough in such cases to 
specify one characteristic which may be a sign of the others. 
We may not be able to mention all the attributes found 



LOGICAL DEFINITION. 49 

in mammals ; but it is a good definition when we say 
that " they are animals suckling their young," for thi,3 
brings out to view a quality common to the whole class, 
and a quality which is the sign of others. 

72* Second Bide. — The definition must be adequate to 
the notion, neither wider nor narrower. If we defined 
grammar the art of speaking a language with propriety, 
the definition would be too narrow, for grammar treats of 
writing a language as well as speaking. If we defined it 
as the science of language, it would be too wide, for 
grammar does not discuss all the scientific questions con- 
nected with language. If we defined Logic as the science 
of our intellectual nature, it would be too wide ; if as the 
science of reasoning, it would be too narrow. 

73. N.B. — The best test of this property of a good 
definition is, that the subject can take the place of the 
predicate, and the predicate of the subject, without any 
change. Thus defining a straight line as the shortest 
distance between two points, we can say the shortest dis- 
tance between two points is a straight line. We can say 
truly ' all poets are men of genius,' but this is no definition, 
for we cannot say all men of genius are poets. 

74. Third Rule. — It is expedient to give the genus as 
well as a characteristic quality. "When we do this we are 
said to define by genua and differentia — that is, characteris- 
tic quality. This cannot always be done, as there may be 
notions which it is difficult to put into a genus in any way 
fitted to clear up their nature. But when it is possible Ave 
should give both the genus and the differentia, as by the one 
we show wherein the notion agrees with others to which 
it is most clearly allied, and by the other we show where- 
in it differs from the notions with which it might be coil- 
founded. In giving a genus it is expedient to give the 
proximum genus. Thus we may define Ethics as "the 
mental science unfolding the laws of man's moral nature ; " 

3 



50 THE NOTION. 

in which " mental science " is the proximum genus, put- 
ting ethics under the same head, as psychology, logic, and 
metaphysics ; and " unfolding the laws of man's moral 
nature" is the differentia, separating it from these de- 
partments of knowledge. 

75. Some important practical rules may be laid down 
as to the language in which the definition should be 
given. The general rule is, that the definition should 
always be clearer than the thing defined. More partic- 
ularly (a) the definition must not be expressed in ambig- 
uous or figurative language, as Aristotle's definition of 
Motion, " the act of being in potency, so far as being in 
potency;" as " matter and mind are sides of one thing." 
(b) It must not contain covertly the name of the thing 
defined, as when we say abstraction is a process in which 
we abstract or draw off, or that life is the sum of the 
vital functions, (c) When the class has positive attri- 
butes, the definition should not be put in a negative form. 
Those who say that infinite is a positive quality, should 
give a better definition of it than when it is said, it is that 
which has no bounds. Naturalists no longer give inver- 
tebrata as the name of a scientific class to be placed 
alongside of vertebrata. 



AIDS TO ABSTRACTION AND GENERALIZATION. 

70. In the employment of abstract and general no 
tions, the mind must always have some sign before it. 
This sign may be 



I -A MENTAL IMAGE OR PHANTASM. 

77. We have occasion, let us suppose, to speak of the 
rose tribe of plants ; as we do so, we may notice that 



TEE MENTAL IMAGE OR PHANTASM. 51 

are have a loose idea, in the sense of image, of a plant 
which may have as many as possible of the characteristics 
of the rose without those of other plants, such as the 
tulip or the lily. Or we have occasion to think of plant 
generally, and we fashion a figure, very possibly with 
axis, branches, and leaves (though there are plants with- 
out these), which may stand for all plants. The image 
may also aid us in our abstractions. When we think of 
great size, we picture a huge bulk ; when of tallness, we 
picture great length ; when of transparency, ice or glass 
with light shining through ; when of wealth, a heap of 
money ; when of dignity, a man of imposing form and 
address ; when of pomp, a dazzling show ; when of mar- 
tyrdom, a person suffering for the truth ; when of mirth, 
a man laughing ; when of sorrow, a person crying. It is 
by help of such images, that children, savages, rustics, in 
fact the great body of ordinary men and women, are able to 
form abstracts and concepts. When such, phantasms can 
be formed, they always render our thinking more lively, and 
therefore more interesting and better fitted to call forth 
emotion. Our pictorial, who are always our most popular 
writers, help our understandings by furnishing concrete 
pictures of abstract notions, and thus enable us to carry 
on our thinking more easily and pleasantly — often, it has 
to be added, more obscurely and confusedly. 

78. These ideas or phantasms are not to be under- 
stood as constituting the abstract or general notion. It is 
usually said of our common notions that they are inade- 
quate. But this is not true of our concepts as exercises ol 
thought ; they may be regarded as adequate, for they are 
of things joined by common attributes, the concept em- 
bracing all objects possessing the common attributes, 
But it holds good of the ideas considered as mental pic- 
tures : we can form no correct image of gravity, or hard- 
ness, or weight, or indeed of any quality. Nor can we 



52 THE NOTION. 

fashion a full phantasm of a concept, for the objects are 
joined by a quality or qualities abstracted, and the ob- 
jects are innumerable. We cannot form a correct picture 
of man in the general, for if we make him white we do 
not include the Negro or Red Indian ; if we make him 
black we leave out the Caucasian race ; and if we make 
him neither black, nor white, nor red, we leave out the 
whole of these three tribes of mankind. In all cases the 
phantasm is to be regarded as a mere sign or representa- 
tion of the result of elaborative thought. It is not of 
the mere phantasm that we make affirmations or denials, 
but of the things for which it stands as apprehended by 
the mind. In certain cases the mental image when used 
as a sign, is quite sufficient to enable us to think accu- 
rately, that is, when it stands for ideas not far removed 
from the singular and the concrete. But when the no- 
tion becomes more and more abstract or general, more 
especially when it is the idea of spiritual objects or qual- 
ities, or when it is a composite one, the formation of a 
mental picture becomes more and more difficult, and at 
last is seen to be altogether impossible. Who can form 
an image, for instance, of law, of truth, of right, of gov- 
ernment, of learning, of civilization ? When we have 
occasion to think of such things, we must call to our aid 
external Signs, and especially Language. 

70. Locke confused himself on this subject by not distinguishing 
between the image and the notion, both of which were embraced in 
bis favorite phrase ' idea,' which, however, he commonly used in its 
literal sense as image. In forming our idea of man or humanity, 
persons leave out that which is peculiar to the individuals, they 
leave out of the complex they had of Peter and James, Mary and 
Jane, " that which is peculiar to each, and retain only what is 
common to them all." (Essay, Booh III, iii, 7.). Bishop Berkeley 
saw the absurdity o/ this view, and not seeing the way out of it, 
lauded himself in nominalism, which thence descended to Hume. 
Stewart, and Whately. " The mind having observed that Peter 
James, and John resemble each other in certain common agree- 



THE MENTAL IMAGE OR PHANTASM. 52 

merits of shape and other qualities, leaves out of the complex or 
compounded idea of Peter, James, and any other particular man that 
which is peculiar to each, retaining only what is common to all, 
and so makes an abstract, wherein all the particulars equally 
partake, abstracting from and cutting off all those circumstances 
and differences which might determine it to any particular ex- 
istence. And after this manner, it is said, we come by the ab- 
stract idea of man, or, if you will, of humanity or human nature ; 
wherein, it is true, there is included color, because there is no 
man but has some color ; but then it can be neither white nor 
black, nor any other particular color wherein all men partake. 
So likewise there is included stature ; but then it is neither 
tall stature nor low stature, but something abstracted from all 
these." Such considerations show that we cannot form an idea of 
man in general in the sense of a mental picture. But they do 
not prove that we cannot form an intellectual conception of objects 
joined by common properties, the conception including all the ob- 
jects possessing the properties. We are thus thrown back on the 
distinction drawn by Aristotle between the phantasm (ipavTcla/ia) 
and notion (vor/fia). The difference between them and yet their 
relation are accurately expressed by him when he says that the 
notion is not the same with the phantasm, and yet is never without 
the phantasm. Norj/iara tlvI dwioei tov /xt) fyavTuoficiTa elvai, tj ovde 
TavTa ipavrda/iara, akV nvn avev Qavrao/iaTup. (He Anim, iii, 7.) 



IL— LANGUAGE. 

SO, Language may be defined as the expression of our 
mental actions and affections by means of words spoken 
or written. The primary benefit derived from it arises 
from its being a means of communicating with our fellow- 
men, and thus enabling us to convey to them our varied 
thoughts and feelings, wants and wishes, and to have theirs 
imparted to us. This is the first and final end of lan- 
guage, subordinating every other, and determining in a 
great measure the changes which it has undergone 
throughout its whole history. But this is not the aspect 
under which we are required to contemplate it in this 



54 THE NOTION. 

work, where we view it simply as the instrument of dis- 
cursive thought. 

81. First. — Language is advantageous, inasmuch as it 
is a sign and register of the abstractions and generaliza- 
tions which mankind are ever forming. We have seen 
that all men are led by a native intellectual tendency, and 
by the circumstances in which they are placed, to separate 
and to combine the objects they meet with ; to distin- 
guish between a thing and its qualities ; to observe the 
relations of things, and then put the things which are re- 
lated into a class. Many of the distinctions thus drawn, 
and groupings fashioned, are valuable only for the mo- 
ment ; but others are of permanent importance, and 
should be carefully preserved ; and this can be done only 
by a name, by what is technically called Denomination. 
A simple illustration or two will enable us to understand 
this. A merchant, say a druggist, has in his warerooms 
a large number of miscellaneous articles lying promis- 
cuously on the floor ; as long as they are in this state he 
feels that he has not absolute command of them ; and 
so he fixes on some ground of distribution and arranges 
them in shelves or drawers on which he puts some kind 
of mark or label. Having done so, he and his assistants 
find that they can at once lay their hands on the article 
they require. Or, a naturalist enters a country the flora 
of which has hitherto been unexplored. As he views 
the profusion before him his first act is to observe, and 
his second is to classify ; but unless he take a third step, 
he is made to feel that all his researches are likely to be 
valueless, if not to himself, at least to others ; he has to 
give a name to the plants which he has put into a class« 
This name finds its way into botanical books, and becomes 
the index of the genus or species to students of every 
country and of all coming ages. These illustrations show 
us the benefit of names in the business of life and in 



LANGUAGE. 55 

natural science. But they serve a like, and, in most 
cases, a vastly more important purpose in regard to all 
the multiplied operations of the mind; preserving (hem, 
when they might otherwise be lost, for our own use and 
that of others ; it may be handing them down to all pos- 
terity, or spreading them over all civilized nations. In 
contemplating the objects which present themselves in the 
world without, and the still more wondrous world withic 
under its divers moods and impulses, mankind fashion an 
infinite variety of thoughts, which can be preserved and 
profitably employed only by the instrumentality of lan- 
guage. 

82. Second. — Language puts us in possession of the 
abstractions and generalizations which have been made 
by other men. In saying so we do not refer to the cir- 
cumstance that it is not so much by personal observa • 
tion as by intercourse with others, that it is by the 
instruction imparted by teachers, companions, and our 
fellow-men generally, and by books ancient and modern, 
that we acquire by far the larger portion of the know- 
ledge possessed by us ; for this proceeds from the pri- 
mary use of language as a means of communication. A 
reference is made under this head, not to the information 
thus conveyed, but to results of discursive thought em- 
bodied in words and phrases. It should be observed 
indeed, that the abstractions and generalizations must 
first have been formed before they could be expressed in 
language. But the name being given it becomes at once 
and forever a sign of the idea. On the word being 
brought under the attention of the young, they ask what 
is meant by it, and are thus put in possession of the 
thought which it may have cost so much pains to ela- 
borate. An intelligent youth hears the phrases ' conser- 
vation of physical force ' and ' correlation of physical 
forces ' employed, and on inquiring into their signification, 



56 THE NOTION. 

he is taught that the amount of force, potential and actual, 
in the universe, is always one and the same, and cannot 
be diminished or increased by any human means, and 
that all the physical agencies, mechanical, chemical, elec- 
tric, and vital, are modifications of that one force. Or he 
hears the word ' aesthetics ' used, and is thus introduced 
to a science which seeks to investigate the laws, subjec- 
tive and objective, of the beautiful and sublime. What is 
thus seen so clearly in science is also manifested in moral 
and practical matters. Some one saw very keenly that 
there is a vast amount of pretension in the world, and 
that there are persons who recommend as great and good 
what is not really so, and gave expression to his percep- 
tion in the word ' humbug ; ' and the phrase goes down 
to posterity because of its felt truthfulness. Some terms 
spring up by a sort of accident and are retained because 
found to be useful ; there is, for example, the word 
' cabal,' made up of the names of persons who were sup- 
posed to have formed a party combination, and the 
phrase has kept its place ever since^ because an ever 
recurring feature of human nature. The British sol- 
diers who had been in the wars of Gustavus Adolphus, 
brought back with them certain terms such as ' plunder,' 
'life-guard,' and ' furlough,' which have ever since been 
retained in our tongue. Thomas Carlyle, with that vig- 
orous grasp of intellect and atrabilious temperament by 
which he is distinguished, in order to show his contempt 
for those who are ever fawning on the great, gave expres- 
sion to what he observed and felt in the word ' flunkey- 
ism,' a phrase likely to go down to all future generations 
To an American custom we owe the phrase 'stump- 
orator,' so descriptive of a style of speaking which cannot 
otherwise be so briefly characterized. 

83. The occupations, the tastes, the habits, indeed the 
whole character of a people, are apt to embody themselves 



LANGUAGE. 57 

in their language. It is said that in Arabic there are 500 
names for a lion, 201) for a serpent, 80 for honey, 400 for 
sorrow, and 1000 for a sword ; and it seems certain that 
there are 5744 relating to the camel. The French have 
given us the words ' finesse,' ' prestige,' ' ennui,' ' foible,' 
' chagrin,' and many others descriptive of their character 
and experience ; and the English have given them in 
return ' jockey,' ' club,' ' sport,' and the phrase ' comfort- 
able,' so expressive of genuine English feeling. The 
Scotch have designated one feature of their national 
character by the word ' canny ; ' and the Irish have ex- 
pressed one of their national traits by the phrase ' blar- 
ney.' A number of words which have of late come in 
upon us with such weight and gravity, such as standpoint 
God-consciousness, claim Germany as their fatherland. 

84 . In holding intercourse with each other, persons fashion or 
modify phrases in accordance with the native tendency of thought, 
and in order to promote mutual convenience. This remark holds 
good, not only of individual words, but of the structure of language 
generally. Hence we have in so many tongues prefixes, suffixes, 
and reduplications ; the gender, number, and case of nouns, and the 
moods and tenses of verbs. These modifications, say declensions 
and conjugations, invented or adopted in the first instance for con- 
venience sake, become in the next generation the means of intro- 
ducing the young to the distinctions of sex, and quantity, and time , 
to the more important relations of things one to another; and the 
contingency, the certainty, and necessity of events. Language thus 
becomes an important means of training the youthful mind to an 
acquaintance with the habitual and useful modes of human thought 
and contemplation. 

85. It is not possible to express the higher forms of thought in 
the language of a people low in the scale of intelligence. In the 
Iroquois there is no word for goodness in the abstract, they have only 
a word for good man. In the Mohican there is no verb for ' I love,' 
the forms involve the subject as well as the action, ' I love him,' ' I 
love you.' In those islands which the Loudon Missionary Society 
has done so much to elevate, there was one word for the tail of. a 
dog, another for the tail of a bird, and a third for the tail of a sheep, 
but no word for tail in general. In Chinese there are terms for 



58 THE NOTIOJH 

elder and younger brother, but none for brother. Christian mis- 
sionaries found great difficulty in fixing on an unexceptionable word 
in that tongue for God, and disputed among themselves as to which 
of the available phrases was the least objectionable. The fixed 
forms of that language and its want of inflections have, I doubt not, 
acted with other causes in keeping that people in a stationary con- 
dition for thousands of years. Notwithstanding the strong attach- 
ment of the people to the Gaelic, the Welsh, and the Irish, it is de 
sirable that these tongues should give way as speedily as possible 
in favor of the English, with its advanced intelligence, its refined 
sentiment, and noble literature. The circumstance that one tongue, 
and this enriched by the thoughts of the highest science, philoso- 
phy, and theology, is used in all the schools of the United States, 
has helped more than any other agency to produce a unity of belief . 
character, and aims, which keeps the people together in spite of the 
many disturbing causes which might make them fly asunder. 

86. The line of thought we are pursuing is fitted to show the 
advantage of being acquainted with more than one tongue. Every 
educated people has fashioned thoughts for itself and embodied them 
in peculiar phrases ; hence the difficulty of translating the words of 
one tongue into precisely synonymous phrases in another. By learn- 
ing the language of a race, we come into possession of their mode of 
thought, which is to us fresh and original. Ennius used to say that 
he had three hearts (the heart being reckoned the seat of intel- 
ligence) because he knew three languages, the Greek, Latin, and 
Oscan. The Emperor Charles V. declared that a person is as many 
times a man as he knows a number of languages. Often do we find 
in other tongues a phrase embodying an idea which never occurred 
to us ; or we are delighted to fall in with the expression of an idea 
which had floated in our minds without our being able to give it an 
exact shape. It sometimes happens that an inaccuracy or confusion 
of thought in one tongue may not occur in another tongue, to which 
we have only to look to have our ideas cleared up. Thus the dis 
tinction between the phantasm and the general notion, drawn by 
Aristotle and known in the middle ages, was lost sight of by the 
English-speaking nations for ages after the time of Locke, who con- 
founded them and expressed them both by his favorite phrase 
'idea.' Of late years the distinction has been revived in our coun 
trv greatly to the benefit of philosophy and specially of logic, by 
bcfolars who noticed, in perusing works of German speculative phi 
lo«ophy, that the two had been distinguished. 



LANGUAGE. 59 

87. Modem European thought has been greatly benefited by the 
Btudy of the ancient classical languages, which commenced in the 
fifteenth century and has been continued to the present time in all 
the higher seats of learning. We have thereby got good not merely 
from the faultless models of brevity, elegance, and taste presented 
by the Greek and Koman writers, but from the very words them 
selves and the ideas embodied in them. We have derived a like — 
in some respects a higher — advantage from the introduction of 
Eastern thought, especially from the Divine thought received from 
the Scriptures with their elevated views of God and holiness — w< 
get the very idea of holiness, or separation from sin, from the Word 
of God, there being no such idea in the writings of Greek or Eoman 
authors. The English language has been farther enriched by ideas 
conveyed by the Italian from the time of Spencer to that of Milton 
by the French in the last century, and by the German in this. Our 
language, like our race, is a happy mixture of very diverse elements : 
while we have as the basis the phrases and inflections of the old 
Saxon tongue, we have made free additions from the Greek and 
from the Latin (either directly or through the Norman French) 
which have introduced us to a more advanced style of thought, and 
a more refined mode of life. 

88. Third. — Language constrains us to give a form to 
thought which would otherwise be loose and vague. 

" Language is a perpetual Orphic song, 
Which rules with Daedal harmony a throng 
Of thoughts and forms, which else senseless and shapeless were." 

Let us try to understand how this takes place. We 
enter a large factory ; we see the complicated machinery, 
the work done, and the persons doing it, and we are filled 
with a general astonishment. Our ideas meanwhile 
may be very indeterminate. But we meet with one ac- 
quainted with the work, and he names the parts one after 
another, the machinery, and the raw materials, and the 
products at the various stages of advancement ; we now 
feel that our notions are becoming clearer. Or, we know 
that after we leave the work we shall be obliged to de- 
scribe it to a friend, and we try to get names for the varied 
apparatus, and to reduce what we have seen to heads. No\? 



60 THE NOTION. 

there is a like process going on, often without our noticing 
it, in the formation of our higher and subtler thought. 
In being obliged to express our thoughts, we have to 
make them definite in order to bring them within the 
forms of settled language. This is specially the case 
when we have to write out our thoughts. " Conference," 
says Bacon, " maketk a ready man," that is, ready to ex- 
press intelligently the thoughts that occur ; " and writ- 
ing an exact man," that is, having leisure to put his 
thoughts into shape, and knowing that others will have 
time to examine them, he has to make them assume a 
more accurate form. How often does a student imagine 
that he has an idea of a subject about which he is read- 
ing, or on which he has heard his teacher lecture, till 
such time as he is examined on it, or has to write de- 
finitely upon it, when he discovers how vague his notions 
have been. It is the great advantage of systematic ex- 
aminations and of essay-writing, that they force the stu- 
dent to understand his topic in order to his being able to 
unfold it in language spoken or written. The interrog- 
ative or maieutic method of Socrates was specially fitted 
to accomplish this end, by constraining the person 
questioned to give his thoughts a definite shape and 
order. 

80. The determinate moulds supplied by language, 
into which to pour our solvent thoughts, are of various 
kinds. Sometimes they are abstractions or analyses, 
which enable and constrain us to decompose concrete or 
complex objects. More frequently they are common no- 
tions, under which we are led or obliged to put single 
objects or lower classes. 

9 O. It is commonly said that language is first synthetic, and then 
analytic. The more correct statement is, that it is first concrete, thai 
is, stands for things with an aggregate of qualities, and then be- 
comes more and more abstract, that is, designates common qualities, 
or objects joined by common qualities. First a word is fixed on to d* 



LANGUAGE. 61 

note an object ; then it is modified by additions, by affixes or suffixes, 
or otherwise, to denote related objects; and then it becomes a root or 
norm of other phrases clustering round it with allied meanings. It is 
in its growth that language becomes synthetic in the proper sense 
of the term, that is, words are joined to express a complexity. 

01. As thought and language make progress, more 
and more is taken in from the void (rb drreigov, as the old 
Greek philosophers called it) ; the waste becomes meas- 
ured and fenced in ; and those who come after must 
accommodate themselves to what their predecessors have 
settled. It thus comes that while language aids thought, 
it tends at the same time to limit and restrain it. In 
using the tongue provided for us, we must fall in with the 
forms which it furnishes. The analyses and generaliza- 
tions of words have, as it were, laid down rails on which 
our thoughts run easily and rapidly, and we are induced 
to travel on these accustomed ways instead of striking 
out new paths for ourselves. This may be one reason 
why the earliest poets of a country — such as Homer and 
.ZEschylus in Greece, Lucretius in Borne, and Dante in 
Italy, and Chaucer and Shakespeare in England — are 
often the freshest ; they looked at things with then* own 
eyes, and not as other men through the eyes of others. 
This may be one of the ends served in Providence by the 
confounding of old tongues and the necessary formation 
of new ones ; as when the northern nations came in upon 
the Roman empire, and Norman French became mixed 
with the Saxon ; the same purpose is served as by the 
mixture of races — the hereditary sameness is disturbed 
and we have a new progeny with fresh life and new char- 
acteristics. Still, the incidental evils arising from a 
language being settled, are as nothing compared with the 
advantages proceeding from a cultivated tongue, which 
pi'ovides innumerable analogies and analyses to stimulate 
and guide thought. Any evils which might arise from a 
slavish adherence to fixed inflections and routine phrases. 



62 ,< TEE NOTION. 

are to be overcome by our forming the resolute determ- 
ination to make language our useful servant without 
allowing it to become our arbitrary master. 

92. Fourth. — Language lightens thought by being 
used as a symbol. When we think of objects not present, 
we must always have some representation of them before 
the mind - This, we have seen, may primarily be a men- 
tal image ; thus when we are thinking about mothers 
generally, we fix on some one mother, say our own, and 
leave out as many of her peculiarities as may make the 
idea stand for mothers generally. But we have shown 
that this phantasm must always be inadequate to represent 
an attribute, or a class comprising an indefinite number 
of objects ; and as the generalizations become wider and 
the abstractions more refined, and when different abstrac- 
tions are mixed with each other, it may be impossible to 
form a picture resembling the reality in the remotest 
degree. Besides, even though we could fashion an ade- 
quate image, it would be sure to distract the mind by 
calling it away to adventitious circumstances. These in- 
conveniences can be obviated only by the use of external 
signs, and particularly of language. 

03. Let us notice how external symbols are fitted to 
lessen the labor of thinking. They do so inasmuch as 
they render it unnecessary to take notice of the unnuin- 
bered objects which go to constitute a class ; as they 
save us from conceiving the attributes which combine 
the objects in the class ; and from thinking of the pecu- 
liarities of the individuals. To illustrate by an example. 
In the natural arrangement of plants there is a sub- 
class, thalamiftorce, from thalamus and flos (flower) ; its 
characteristics are said to be " calyx and corolla pres- 
ent, petals distinct, inserted into the thalamus or recep- 
tacle, stamens hypogynous." Now had this tribe oi 
plants not received a name, we should have beei 



LANGUAGE. 63 

Dbliged, every time we thought or spoke about them, to 
represent to ourselves or enumerate to others their 
various characteristics, and we should have been forced 
to endeavor to conceive of the numberless plants be- 
longing to the class ; and as we tried all this, we should 
have found ourselves distracted and overwhelmed. This 
burdensome work is avoided by using the phrase thalami- 
floroe to stand for the whole tribe. 

04. As feeling the convenience of it, and as being en- 
dowed with the organs of speech, and the mental capa- 
city and inclination to employ them, man naturally and 
spontaneously betakes himself to words, to stand for 
thoughts and things. " It is not necessary, even in the 
strictest reasonings, that significant names which stand 
for ideas, should every time they are used create in the 
understanding the ideas they are made to stand for. In 
reading and discoursing, names are for the most part 
used as letters are in algebra, in which, though a partic- 
ular quantity be marked by each letter, yet to proceed 
right it is not requisite that in every step each letter 
should suggest to your thoughts that particular quantity 
it was appointed to stand for." (Berkeley.) In many 
processes of thought, the attention seems to be very much 
fixed on the verbal sign ; and conception comes to be what 
Leibnitz calls Symbolical. Words come to be used like 
algebraic symbols, a, b, c, which stand for quantities 
without our thinking of any particular quantity, like 
counters which represent money, like bank-notes which 
stand for gold. The mind yields willingly to this state 
of things, as feeling how much the memory and the power 
of imaging and apprehending are thereby eased. We do 
not choose every time we use such words as liberty, in- 
dependence, order, civilization, virtue, commonwealth, 
church, religion, to think of all that is comprised in them. 
We pass them on as the banker gives away a hundred 



64 THE NOTION. 

pound note, or a hundred dollar bill, without thinking ot 
the gold it stands for ; or as we receive it without con- 
ceiving how many articles of utility or of comfort it would 
purchase. Language is thus a species of stenography by 
which the mind lightens its labors and makes its higher 
efforts less irksome. 

95. Fifth. — It follows as a corollary, that by means of 
language we can carry on thinking to a greater extent 
than we should otherwise be able to do. 

We do not allow indeed, that language, or even that 
external signs, are necessary to thought. It is forever 
rung in our ears by certain writers, that there could be 
no reasoning, no thought of any kind, without language 
Dugald Stewart goes so far as to maintain, that c: without 
the use of signs our knowledge must have been confined 
to individuals, and that we should have been perfectly in- 
capable both of classification and general reasoning ; " and 
" lays it down as a proposition which holds without any 
exception, that in every case in which we extend our 
speculations beyond individuals, language is not only a 
useful auxiliary, but is the sole instrument by which they 
are carried on." This is a very extreme position, pro- 
ceeding on a doctrine which tends to degrade the human 
faculties, and which has been most eagerly maintained by 
those who derive all men's ideas from sensation. In op- 
position to it I lay down the counterpart statement, that 
without thought language could not be fashioned, could 
not be understood, could not be intelligently employed. 
" Parrots," says Locke, " will be taught to make articulate 
sounds enough, which yet are by no means capable of lan- 
guage. Besides articulate sounds, therefore, it was farther 
necessary that man should be able to use these sounds as 
signs of internal conceptions, and to make them stand as 
marks of the ideas within his mind." " From whence it 
follows," says his critic, M. Cousin, " that language is not 



LANGUAGE. 65 

the product of sounds, that is to say, of the organs and 
the senses, but of the intelligence ; 2. That the intelligence 
is not the product of language, but, on the contrary, lan- 
guage is the product of intelligence ; 3. That the greater 
part of the words having, as Locke well remarks, an ar- 
bitrary signification ; not only are languages the product 
of the intelligence, but they are even in great part the 
product of the will ; while *in the system that has pre- 
vailed both in the school of Locke and in a school alto- 
gether opposed to his, intelligence is made to come from 
language ; in the latter, without much inquiring whence 
language comes, in the former, by making it come from 
the sensation and the sound, without suspecting that 
there is a gulf between the sound considered as a sound 
and the sound considered as a sign, and that what makes 
it a sign is the power to comprehend it, that is, the 
mind, the intelligence." 

OS. Two circumstances show that the mind can reason 
without language. One is, that we can point out cases in 
which there is reasoning without words. An experienced 
seaman looking on the sky, which to our eye seems so 
calm, utters something about a storm. We ask what he 
means, and his explanation only renders the subject more 
confused. But we know what he intended when a few 
hours after we see an angry sea, and find the waves lash- 
ing on the vessel as if bent on sinking it. There has cer- 
tainly been a process of reasoning, and the logician could 
state it in syllogistic form ; but it is doubtful whether 
language has been of any use in enabling him to conduct 
it. Another circumstance is, that infants reason. Eefer- 
ring to the view of those who deny the possibility of 
reasoning of any kind without the aid of general terms, 
Dr. Brown says : " As if the infant, long before he can be 
supposed to have acquired any knowledge of terms, did 
not form his little reasonings on the subjects on which it 
5 



66 THE NOTION. 

is important for him to reason, as accurately probably as 
afterwards, but at least, with all the accuracy which is 
necessary for preserving his existence and gratifying his 
few feeble desires. He has, indeed, even then, gone 
through processes which are admitted to involve the 
finest reasoning by those very philosophers who deny 
him to be capable of reasoning at all. He has already 
calculated distances, long before he knew the use of a 
single word expressive of distance, and accommodated 
his induction to those general laws of matter of which he 
knows nothing but the simple facts, and his expectation 
that what has afforded him either pain or pleasure, will 
continue to afford him pain or pleasure. What language 
does the infant require to prevent him from putting his 
finger twice in the flame of that candle which has burned 
him once? or to persuade him to stretch his hand, in 
exact conformity with the laws of optics, to that very 
point at which some bright trinket is glittering on his 
delighted eye ? To s appose that we cannot reason with- 
out language, seems to me, indeed, almost to involve 
the same inconsistency as to say that man is incapable of 
moving his limbs till he have previously walked a mile " 
{Led. : XLYII.) 

9t. Such considerations show that, 

" Thought leapt out to wed with thought, 
Ere thought could wed itself to speech." 

And then have we not all had thoughts and sentiments 
which, so far from being the product of words, we have 
felt it to be impossible to translate into words, and we 

have reason to complain, 

" Oh dearth 
Of human words, roughness of mortal speech.'' 
Our men of profoundest thought and deepest feeling, 
have ever striven to rise above human phrases and gaze 
directly upon realities. 



LANGUAGE. 67 

" Words are but under agents in their souls ; 
When they are grasping with their greatest strength 
They do not breathe among them." 

This does not prove, on the opposite side, that even such 
thoughts might not be made more definite, and therefore 
more thoroughly significant, by being expressed in words ; 
it simply shows that language, with all its refinements, 
does not come up to the extent ard variety of thought. 

,98. It should be freely allowed that very much of our 
thinking is carried on by means of language. We have 
already had before us the circumstances which furnish an 
explanation. Though, in the order of the formation of 
language, the notion comes before the name, yet it is com- 
monly by the name, at least in countries richly supplied 
with common terms, that the notions are first gained. 
The name and the notion are thus indissolubly associated 
in our minds, so that there is never the one without the 
other. Then, as feeling the notion to be complex and a 
burden upon our conceptive power, we prefer thinking by 
the simple word rather than be at the trouble of appre- 
hending all that is involved in its signification. 

09' While we can think and reason without words, we 
are all the better of language in every case, and in many 
complicated operations we should be lost as in a laby- 
rinth without signs of some description. Even in the 
apprehending of abstract and general notions, we are the 
better of names ; but we especially need them when we 
come to compare our notions, either immediately in Log- 
ical Judgment, or mediately in Reasoning. The botan- 
ist, let us suppose, is comparing two classes of plants, one 
whose characteristics have already been given, and the 
other thus described : — " Sepals 4, deciduous, the twu 
lateral ones gibbous at the base : stamens 6, tetradyna- 
mous.' - How troublesome would it be to specify these 
marks every time we had occasion to consider or speak of 



68 THE NOTION. 

the relation of these two tribes of plants. "We are 
saved from all this by having a name for each of the 
groups ; the one is called thalamiflorce, and the other 
cruciferce, and the relation between them is expressed 
by saying that the cruciferce are an order under the sub- 
class thalamvflorce. 

100. And if language be useful in judgments in which 
we have only two notions, it is still more advantageous in 
reasoning, in which we have three notions. In order to 
see the utility of symbols in reasoning, we have only to 
consider that all inference, except in a few simple cases, 
implies one or more class notions. It proceeds, as we 
shall see, on the principle that whatever is predicated of 
a class, may be predicated of all the members of the class. 
In all cases there is a class notion in the argument, and 
in many cases all the three notions compared, minor, 
major, and middle, are general. How cumbersome should 
we find it, were we obliged in every argument, to consider 
the indefinite individuals and the common marks that 
combine them in every concept. And when in our ratio- 
cinations there is not only one argument but a chain of 
arguments, each containing one, two, or it may be three 
new concepts, with their numerous individuals and their 
combining attributes, I believe the mind would feel itself 
utterly bewildered and oppressed without the use of sym- 
bols to stand for the classes. 

101. In thinking with the assistance of words, we can 
pass as far beyond thought conducted by mere mental 
signs, as by numbers we go beyond counting with the 
fingers, and by algebra beyond arithmetical computations. 
The transmission of messages by the electric telegraph 
hundreds of miles in a few seconds, is an outward picture 
of the rapidity with which the most remote and recondite 
thoughts may be brought into communion by the refined 
phrases of a cultivated language. " Though we should be 



LANGUAGE. 09 

capable of reasoning without language of any sort, and of 
reasoning sufficiently to protect ourselves from obvious 
and familiar causes of injury, our reasonings in such cir- 
cumstances must be very limited, and as little compa- 
rable to the reasoning of him who enjoys all the new 
distinctions of a refined language, as the creeping of a 
diminutive insect to the soaring of an eagle. Both ani- 
mals, indeed, are capable of advancing, but the one passes 
from cloud to cloud, almost with the rapidity of the 
lightning which is afterwards to flash from them, and 
the other takes half a day to move over the few shrunk 
fibres of a withered leaf." (Brown.) 

102. Sixth. — It is one of the special advantages of 
language that it helps thought to make progress. This is 
very happily brought out by Sir W. Hamilton : " A sign 
is necessary to give stability to our intellectual progress 
— to establish each step in our advance as a new starting- 
point for our advance to another beyond. A country may 
be overrun by an armed host, but it is only conquered 
by the establishment of fortresses. Words are the for- 
tresses of thought. They enable us to realize our do- 
minion over what we have already overrun in thought — to 
make every intellectual conquest the basis of operations 
for others still beyond. Or another illustration : You 
have all heard of the process of tunnelling, of tunnelling 
through a sand-bank. In this operation it is impossible 
to succeed unless every foot, nay, almost every inch, in 
our progress be secured by an arch of masonry, before 
we attempt the excavation of another. Now, language 
is to the mind, precisely what the arch is to the tunneL 
The power of thinking and the power of excavation are 
not dependent on the word in the one case, nor on the 
mason -work in the other ; but without these subsidiaries 
neither process could be carried on beyond its rudimen- 
tary commencement. Though, therefore, we allow thai 



70 THE NOTION. 

every movement forward in language must be determined 
by an antecedent movement forward in thought ; still, un- 
less thought be accompanied at each point of its evolution 
by a corresponding evolution of language, its further de- 
velopment is arrested. Thus it is that the higher exertions 
of the higher faculty of Understanding, the classification 
of the objects presented and represented by the subsidiary 
powers in the formation of a hierarchy of notions ; the 
connection of these notions into judgments ; the inference 
of one judgment from another ; and, in general, all our 
consciousness of the relations of the universal to the par- 
ticular, consequently all science strictly so denominated, 
and every inductive knowledge of the past and future 
from the laws of nature : not only these, but all ascent 
from the sphere of sense to the sphere of moral and re- 
ligious intelligence, are, as experience proves, if not alto- 
gether impossible without a language, at least possible to 
a very low degree." 



INCIDENTAL DISADVANTAGES OF LANGUAGE, 

103. Bacon directed the attention of modern thinkers 
to that subject in illustrating the Idola Fori, or those 
which arise from the intercourse of mankind one with 
another. " Though we think we govern our words, yet 
certain it is that words, as a Tartar's bow, do shoot back 
upon the understanding and do mightily entangle and 
pervert the judgment." The subject thus opened has 
been prosecuted by Hobbes, by Locke, by the French 
school of Condillac, by Stewart, by Whately, and others, 
some of whom trace almost all errors to the influence of 
language. Locke has dilated on this subject (JEs^ay, B. 
OT.), and has offered many valuable cautions, but often 
exaggerates the evils. "He that shall well consider the 



LANGUAGE. 71 

errors and obscurity, the mistakes and contusion that are 
spread in the world by the ill use of words, will find 
some reason to doubt whether language, as it has been 
employed, has contributed more to the improvement or 
hindrance of knowledge among mankind." When men'? 
ideas are confused, the language they employ will also be 
confused, and thus increase the confusion — just as when a 
master does not thoroughly organize his household, the 
servants instead of aiding him will throw everything into 
disorder. Examples of the evil influence of terms, are 
often taken from imperfectly formed sciences, material 
or mental ; but there the error has sprung from the state 
of the department of knowledge ; and when the science is 
properly constructed by its appropriate means, inductive 
or deductive, it soon finds an appropriate nomenclature. 

104:. M. Cousin, in criticising Locke, lias some fine remarks on 
this subject. " The question is, does all error spring from language> 
and is science nothing else than a well-constructed tongue ? No : 
the causes of our errors are very different, both wider and deeper. 
Levity, presumption, indolence, precipitation, pride, and thousands 
of causes influence our judgment. The evils of language may join 
on to natural causes and aggravate them, but do not constitute them. 
If you consider them, you will see that the greater part of disputes 
which appear to be about words, are, at the bottom, disputes about 
things. Humanity is too earnest to trouble itself and shed its 
purest blood for words. Wars do not turn on disputes about words ; 
they rise from other quarrels — from quarrels theological and scien- 
tific, of which they mistake the depth and importance who resolve 
them into pure logomachies. Assuredly all science ought to seek 
a language well constructed ; but it is to take the effect for the 
cause, to suppose that sciences are well constructed because lan- 
guages are well constructed. The contrary is the truth ; the 
sciences have well-constructed languages when they themselves are 
well constructed." He illustrates this by mathematics, where the 
terms are good because the ideas are thoroughly determined ; and 
by such departments as medicine, where we must first employ care- 
ful observation and rigid reasoning, and then the appropriate no 
uaenclature will be furnished. 



72 THE NOTION. 

105. But it should be frankly allowed that words, 
while they are generally a great help to thought, do often 
hinder it. It may serve some good purposes to consider 
the evils which arise from the abuse of language. In do- 
ing so we shall not dwell on the intentional perversion of 
words by the sophist, the flatterer, the politician. For 
these abuses language is not responsible ; though it is 
true that the ambiguous nature of words very much aids 
the liar and equivocator, and lends some plausibility to 
the saying that language is rather an instrument for con- 
cealing thought. 

100. (1.) There is the vagueness of so many phrases. 
How this should be, the observations we have made on 
the formation of notions may enable us to understand. In 
forming abstract terms, we join an aggregate of attri- 
butes having a merely superficial and no deep or intimate 
relation in the nature of things, or more frequently with- 
out knowing what are the attributes comprised ; and then 
we make unwarranted assertions regarding that term, 
saying of one part what is true only of another, or of the 
whole what is true only of a part. Again, what has been 
represented (§ 24) as the second essential step in general- 
ization is often performed very imperfectly. We perceive 
a general resemblance, and we form a class, and we give 
a name ; but meanwhile we have not fixed, except in a 
loose way, on the points of resemblance, and the phrase 
goes into circulation carrying its dross with it. Then it 
is to be taken into account, that in our first generaliza- 
tions we may fix on the superficial rather than the deeper 
properties of things. Thus the word money meant orig- 
inally articles used in exchange, and then was applied to 
coin ; in time it came to have a larger and more scientific 
meaning ; but the ambiguity led the popular mind to 
identify money with wealth, to conclude that a country 
must be enriched by increasing its coin, and by passing 



LANGUAGE. 73 

laws against the exportation of money. It is one of the ad- 
vantages arising from science, from honest discussion, and 
the progress of thought generally, that it gives greater 
precision to language by compelling us to distinguish the 
diverse things wrapt up in one complex phrase, and to 
get a separate term for each. It was disputed whether 
the syllogism was or was not an invention of Aristotle, 
and both parties were right and both wrong according to 
the use they made of the term. Such discussions led to 
a distinction being drawn between invention and dis- 
covery, the former being confined to the devising of some- 
thing new, and the latter to the finding out of what 
before existed : and we now deny that Aristotle invented 
the syllogism, while we claim for him that he discovered 
it to be the form to which all reasoning can be reduced. 
The ancients, and the moderns down to the middle of last 
century, used the word Sensation to denote both the 
knowledge and the sensitive feeling got through the- 
senses ; Reid drew the distinction between Sensation and 
Perception ; and now, to avoid ambiguity, we employ the 
phrase Sense-Perception to designate both. It is thus we 
are getting new notions and new distinctions to super- 
sede or supplement the old ; and a permanence is im- 
parted to them by their being stamped with names. 

107 • (2.) There are different meanings and shades of 
meaning attached to a word. It is not difficult to under- 
stand how this should originate. Every word has a his- 
tory. If it could speak for itself, instead of being a mere 
unconscious instrument in the hands of a higher power, 
it might furnish us with a biography. In doing so, it 
would have to commence with its genealogy. Many 
words might furnish us with an older one than the most 
ancient nobility. Some could point to their ancestrv 
among the Roman patricians ; some go back to the 
Greek gods and demigods ; while others ascend to the 



74 THE NOTION 

Hebrew patriarchs and prophets ; not a few boast that 
they come to us from Paris with the last new fashion ; 
while a considerable class bring with them the broad 
sense and deep thought of Germany. Our tongue is en- 
riched by these constant importations. But it is to be 
expected that in such a mixture of emigrants there should 
be some whose character is very ambiguous. There is 
the word 'idea/ which has had so many meanings : des- 
ignating now an image, now an eternal model, now a con- 
cept, now an intuitive truth ; and the most satisfactory 
judgment we can pronounce upon one which has had so 
many aliases is, that it should be banished altogether from 
the commonwealth of philosophy — where it has wrought 
only mischief — leaving it still a place in common conver- 
sation and in poetry. "With some, Keason stands for the 
undefined qualities possessed by man and not by brutes ; 
with others, it signifies much the same as understanding 
or intelligence, and including the process of reasoning ; 
with others, and especially with the higher metaphysi- 
cians of Germany, denoting the capacity which discovers 
necessary truth immediately, as distinguished from the 
logical understanding which proceeds discursively, — in 
this last sense reason and reasoning are contrasted. 

108» The perplexity is increased by the circumstance 
that the phrase has one meaning in one age, and another 
in another age. Unwilling to offend prejudice, and to 
give their writings an affected and repulsive aspect, our 
fresh thinkers retain the old phrase, while they alter the 
meaning to suit the new aspect of truth to which they 
would introduce us. " We have resolved to accompany 
antiquity as far as possible, since we are anxious, so far 
as it can be done with the pen, to make an alliance be- 
tween what is old and new in learning. We therefore 
retain old terms, though we often alter their meaning 
and definitions, according to that moderate and laud- 



LANGUAGE. 75 

able mode of innovating in civil affairs whereby the con- 
dition of things being changed, the usual names are re- 
tained ; as Tacitus remarks regarding the names of the 
magistrates which were retained even when the offices 
were somewhat changed." (Bacon.) This circumstance 
has bred great confusion. Thus the word Form as dis- 
tinguished from Matter, has been used in one sense by 
Aristotle, in another by Bacon, in a third by Kant 
From the time of Aristotle to that of David Hume and 
Kant, to argue ' a priori,' meant to proceed from 
cause to effect, or from reason to consequent ; and to 
argue ' a posteriori,' to proceed from effect to cause, and 
from consequent to reason. Since the rise of the Kant 
ian philosophy, by the ' a priori ' method is meant pro- 
ceeding from principles imbedded in the mind and inde- 
pendent of experience. 

In the former sense, the famous argument of Samuel Clarke for 
the existence of God would be called a 'priori, as it proceeds from 
reason to consequent ; but in the latter sense it is partly a 'posteriori, 
inasmuch as arguing frcm our idea of space to a being of whom 
space is an attribute, it proceeds on the fact that man has an idea of 
space. 

109. Little evil would arise from this provided we 
always distinguished between the meanings. But one 
use of names, we have seen, is to save us from imaging or 
remembering all the objects and properties denoted by 
them. But hi the use of ambiguous phrases, especially 
in abstract discussion, we are apt unconsciously to slide 
from one meaning to another ; and we make an affirma- 
tion or denial of a word, using it, in the rapidity of 
thought, in one sense, whereas the predication would be 
valid only if we used the phrase in another sense. The 
ambiguity of the words 'idea,' 'a priori,' 'reason,' has 
helped to prolong the discussion as to whether there are 
innate ideas, a priori truth, and an intuitive and inde- 
pendent reason in the human mind. 



76 THE NOTION. 

110. The greater number of the words in our language have come 
down to us from a rude and simple state of society, and they bear 
the impress of their origin, — resembling in this respect the man who 
has risen in the world from the lower ranks, and is now admitted, 
because of his talents and success, to the most polite circles, but who 
has not been able to shake himself free from the manners of his 
youth. This, in some aspects, is a disadvantage, as it allows less 
accuracy of language and thought. To avoid the evil, we very 
properly bring in terms from the dead classical languages, to express 
rigidly exact scientific truth. But seen in another light, it is a bene 
fit that our language has sprung from a less artificial condition of 
things, — just as the most polished circles are all the better of the 
occasional introduction of persons whose manners, if not so refined, 
are, at least, more fresh and natural. These old home-born phrases, 
if not so fitted to express abstract truth, are more effective in evok- 
ing genuine and heart-born feeling. I can conceive that some lan- 
guages, like the manners of some men, might become too artificial. 
The most perfect tongue is that which has both elements, which 
Beeks to retain the freshness of youth in the midst of the maturity 
of age. 

111. (3.) There are words that mislead us by their 
associations. Such are phrases which stir up feeling, 
pleasant or tumultuous. "Who can reason calmly when 
the appeals made deal in such words as home, native 
land, liberty, independence. Any evil thus arising may 
be counteracted by the ennobling influence produced by 
the ideas thus suggested ; but it is different when the 
language raises up passions which agitate the soul as the 
wind does the ocean, or lusts which pollute it by sinking 
it in the mire. Again, there are phrases used by our old 
authors which were not offensive iu their day, but are felt 
by us to be coarse and indelicate. As illustrating the 
same point, we may refer to the fallacies into which men 
fall from " usually taking for granted that paronymous 
(or conjugate) words, i. e., those belonging to each other, 
as the substantive, adjective, verb, &c, of the same roots, 
iiave a precisely correspondent meaning ; which is by no 
means universally the case." (Whately.) As examples 



LANGUAGE. 77 

we may give art and artful, design and designing, theorj 
and theorist, scheme and schemer. Thus a man is repre- 
sented as having an art, a design, a theory, or a scheme, 
and we look upon him as artful, a designer, a theorist, or 
a schemer. Home Tooke, the grammarian, argued from 
the derivation of the word ' true,' that there could be " no 
such thing as eternal, immutable, everlasting truth." 
"True," as we now write it, or trew as it was formerly 
written, means simply and merely, that which is trowed, 
ind instead of being a rare commodity on earth, except 
mly in words, there is nothing but truth in the world." 
Two persons may contradict each other and yet both 
speak the truth, for the truth of one person may be op- 
posite to the truth of another. To speak truth may be 
a vice as well as a virtue." 

112. Under this same head we may place the mislead- 
ing influence of words which now denote mental acts, but 
which were originally applied to material objects. Thus 
' idea ' meant originally an image ; ' apprehension ' and 
' conception ' are derived from the act of taking hold of a 
thing ; ' understanding ' signifies something placed be- 
neath ; ' substance,' that which stands beneath ; and 
'spirit,' in a number of tongues, air or breath. Since 
mind and body are called substances, some have argued 
that in addition to the mind and body which we know, 
and know as having being, permanence, and potency, 
there must be something standing under them. It is 
difficult for those whose thoughts are habitually em- 
ployed about sensible things to conceive of spiritual 
truths, and the difficulty is increased by the circumstance 
that the language in which they are expressed was at 
first materialistic, and is still apt to call up sensible 
images. 

113. (4.) We are led by the advantages which lan- 
guage supplies to use words without inquiring into their 



78 THE NOTION. 

meaning. This is in itself the greatest of all the evils, 
and is the source, directly or indirectly, of most of the 
others. We have seen that it is one of the main pur- 
poses served by symbols, that they render it unnecessary 
to conceive all that is in the notion, all its objects, and all 
its marks. But then, just because language so eases thought 
aud labor, we come to give up rigid inquiry and allow 
words to guide us at their will or caprice. This is one 
reason why mankind are so apt to follow hereditary or 
popular beliefs embodied in cherished phrases. " Men," 
says Locke, " having been accustomed from their cradles 
to learn words which are easily got and retained, before 
they knew or had framed the complex ideas to which they 
were annexed, or which were to be found in the things 
they were thought to stand for, they usually continue to 
do so all their lives ; and without taking the pains neces- 
sary to settle in their minds determined ideas, they use 
their words for such unsteady and confused notions as 
they have, contenting themselves with the same words 
other people use, as if their very sound necessarily carried 
with it constantly the same meaning. This, though men 
make a shift with in the ordinary occurrences of life, 
where they find it necessary to be understood, and, there 
fore, they make signs till they are so ; yet this insignifi- 
cancy in their words, when they come to reason concern- 
ing either their tenets or their interest, manifestly fills 
their discourse with abundance of empty unintelligible 
noise and jargon, especially in moral matters, where the 
words, for the most part, standing for arbitrary and nu- 
merous collections of ideas, not regularly and permanently 
united in their nature, their bare sounds are often only 
thought on, or at least very obscure and uncertain no- 
tions annexed to them." 

114. The question arises, how are these evils to be 
avoided ? It is evident that it is not to be done by dio- 



LANGUAGE. 79 

carding the use of language — which would be like putting 
out one's eyes in order to avoid mistakes in vision. Ad- 
vantage may arise from attending to some such rules as 
the following : 

First. Let us begin with ascertaining the meaning of the 
word. We may do this by the help of a dictionary ; or by 
looking to the sense in which it is used by those who in- 
telligently employ it, more specially by resorting to the 
writings of those who treat expressly of subjects in which 
it ought to be accurately employed. 

115. Second. When a word is ambiguous, we should 
make ourselves acquainted with the various senses in 
which it is used, not only by the writer whose works we 
are reading, but those in which others, or in which we 
ourselves, have been accustomed to employ it. If we 
have not before us the various senses and the difference 
between them, we shall ever be tempted to slide from the 
one to the other without knowing it. Thus, in mental 
philosophy, we must never lose sight of the various 
senses in which the phrases 'idea,' 'a priori,' c a pos- 
teriori,' ' experience,' ' form ' and ' matter,' ' subject ' and 
' object,' ' conditioned ' and ' unconditioned/ are em- 
ployed. If we neglect this, we are certain to be led 
astray by the errors which lurk beneath these phrases, 
all of which have been used in different senses and been 
the vehicles of false doctrines. 

116. Third. We must be at pains to settle the precise 
notion which the word stands for. This implies much 
more than a dictionary understanding of it. It requires 
that we go back to the notion in the mind. For every 
term stands primarily for an apprehension of the mind ; 
that apprehension must, no doubt, be of objects, but it is 
of objects apprehended, and so we must look first at the 
apprehension, and then compare it with the things. This 
is a counsel frequently pressed by Locke. " A man 



80 THE NOTION. 

should take care to use no word without a signification, 
no name without an idea for which he makes it stand. 
This rule will not seem altogether needless, to any one 
who will take the pains to recollect how often he has met 
with such words as instinct, sympathy, antipathy, &c., in 
the discourse of others, so made use of as he might easily 
conclude that those that used them had no ideas in their 
mind to which they applied them ; but spoke them only 
as sounds, which usually served instead of reasons, on the 
like occasions. Not but that these words, and the like, 
have very proper significations in which they may be 
used, but there being no natural connexion between any 
words and any ideas, these and any others may be 
learned by rote and pronounced or writ by men who 
have no ideas in their minds to which they have annexed 
them, and for which they make them stand ; which is 
necessary they should, if men would speak intelligibly 
even to themselves." " Justice is a word in every man's 
mouth, but most commonly with a very undetermined, 
loose signification, which will always be so, unless a man 
has in his mind a distinct comprehension of the compo- 
nent parts that complex idea consists of : and if it be de- 
composed, must be able to resolve still on, till he at last 
comes to the simple ideas that make it up ; and unless 
this be done a man makes an ill use of the word ; let it be 
justice, for example, or any other. I do not say a man 
need stand to recollect and make this analysis at large, 
every time the word justice comes in his way ; but this 
at least is necessary, that he Lave so examined the signi- 
fication of that name, and settled the idea in all its parts 
in his mind, that he can do it when he pleases." 

117> Fourth. — Let us observe whether the notions are 
Singulars, or Abstracts, or Universals. We are reading, 
let me suppose, of beauty, and we are anxious to have 
3lear ideas on the subject. Let us first inquire what sort 



LANGUAGE. SI 

of notion is denoted by the word. We easily and at once 
discover that it is an Abstract notion, and therefore we 
do not for one instant supposev that it has, or can have, a 
separate existence. We are not, on the other hand, 
rashly to conclude that it has no existence. It is a 
reality, but a reality in objects ; and we are led to look 
to objects and inquire what it is in them that we desig- 
nate by this name. 

Or the word we have occasion to employ is a General 
one. We have now to inquire what is the class of ob- 
jects connoted by it, and what the common qualities in 
respect of which they are grouped. The word used, I 
shall suppose, is ' instinctive ; ' it is said of such an ac- 
tion that it is ' instinctive.' We proceed on the idea that 
it points to a reality ; but we do not suppose that it is a 
reality distinct from the beings possessing it : we look 
for it in the living beings endowed with it, and we pro- 
ceed to inquire what it is, whether it is a single property 
or, as is more probable, a number of properties adapted 
to each other and tending to one end. 

When the notion is what I have called a Generalized 
Concrete one, we are to bear in mind that we cannot 
expect to exhaust all the properties of the objects em- 
braced in the class. It was foolish and vain to seek, as 
Socrates seems to have done, for some one thing as con- 
stituting the to ov of a % class notion, say the to aaXbv ; or 
as the schoolmen did, to specify the essence of every uni- 
versal, as, for instance, of man. 

118* It is of great moment to take these cautions with 
us in all our higher thinking, in which we are ever tempt- 
ed to look upon abstractions as independent wholes. The 
ancient Greek philosophers often gave a separate existence 
to the abstractions fashioned by them. Thus the Elea- 
tics, and Plato after them, were accustomed to discuss the 
nature of to ov, or being, as if it were a distinct sub- 
6 



82 THE NOTION. 

stance like mind or body. We have fallen into a like 
mistake in modern times. We speak very properly of the 
faculties of the mind, such as the memory, the imagina- 
tion, and judgment ; but then we are led to think and 
write about them as if they were acting entities, whereas 
they are merely capacities of the thinking mind. We 
find ethical writers speaking of virtue as if it were some- 
thing separate from and above the virtuous mind ; where- 
as it is a mere attribute of virtuous agents, from which it 
cannot be separated except in mental abstraction. Some 
write about gravitation as if it had an independent exist- 
ence, whereas it is a mere property of matter having no 
existence separate from individual, bodies. Again, gen- 
eral terms are apt to be regarded as singulars. Men 
speak and reason as if general phrases pointed to some 
one existence, whereas they merely connote a class of 
things having one or more points of resemblance. Some 
discourse about the laws of nature, as if they were some- 
thing different from the objects in the universe, whereas 
they are generalizations of the modes in which the objects 
operate. Having begun with this blunder in thought, 
there are some who go a step farther and make the laws 
of nature a substitute for Deity. They have first given 
them an existence separate from God's works, and having 
got such a convenient mode of accounting for these 
works, they feel as if nature could work without God al- 
together. We are reminded of an analogous error. We 
employ the word ' nature ' as a convenient one to denote 
the whole knowable creation as it comes from God's 
hands. But we forget that the phrase is merely a generic 
one, and then are led to talk of nature as haying an 
existence separate from the combined works of God. 
Having given it an independent existence we end by 
deifying it — I fear nature is the only God worshipped b\ 
many of the votaries of physical science in our day. 



LANGUAGE. 8H 

110. Fifth. — We must carefully consider the things 
from which the notions have been formed. I believe, in- 
deed, that we ought first to look to the notions, for words 
stand primarily for apprehensions of the mind. But ap- 
prehensions, so far as they profess to be drawn from 
things, must conform to them, and in order to see 
whether our notions are accurate and adequate, we must 
over compare them with the things from which they are 
derived. We have seen that the great English metaphy- 
sician has done signal service to philosophy by insisting 
that we always rise from terms to the ideas they stand 
for. But another English philosopher has, if possible, 
conferred a greater benefit by requiring that we should 
ever go beyond notions to things. Bacon complains, I be- 
lieve justly, of the ancient Greek philosophers and of the 
scholastic logicians, that they looked at names which had 
no corresponding objects, or at notions abstracted from 
things ; that their very definitions consist of words, and 
" verba gignunt verba. Verba notionum tesserse sunt, quare 
si notiones ipsoe (quae verborum animoe sunt) male et varie 
abstrahantur tota fabrica corruit." And so he recom- 
mends the observation of things by a careful induction as 
the means of attaining truth and certainty ; and in doing 
so has given a nobler contribution to the science of Logic, 
in the enlarged sense of the term, than any other except 
Aristotle. 



LAWS OP THOUGHT INVOLVED IN THE USE OF SIGNS. 

120. First Law. — Every Term stands for a Notion, 
which must be either a Singidar Concrete, an Abstract, 
or a Universal. We should accustom ourselves, in think- 
ing, to look more to the notion than the phraseology, and 
we should ever be ready to translate our words into 



84 TEE NOTION. 

thoughts. But if the analysis which we have given of 
notions be correct, these terms when turned into no- 
tions will be found to be one or other of our threefold 
division : they will be Percepts or of single things thought 
of in the Concrete ; or Abstracts, that is of qualities ; 01 
Concepts, that is of a class of objects joined by common 
qualities. Now it is often of great moment in discussing 
a complicated subject, that we should know precisely to 
which of these classes the notion which we are using be- 
longs, and that we should understand it, and use it ac- 
cordingly. If we neglect this, if we employ, for example, 
abstract and general terms as if they were singulars, or 
treat abstract and general terms as if they had no sort of 
reality, we shall find ourselves involved first in inextri- 
cable confusion, and then in positive error. 

12 I. Second Law. — We can predicate of the Sign only 
what might be predicated of the Notion. "We have seen 
that after we have denoted a notion by a sign we can 
judge and reason about the sign without thinking of all 
that is signified by it. But we must not allow ourselves 
for one moment to suppose that the sign has acquired 
any new power not found in that which it stands for, or 
that we are at liberty to affirm or deny of it what we 
would not affirm or deny of the notion itself provided it 
stood fairly before us. If A stands for a square number, 
we are not allowed to predicate of it what we could not 
predicate of the square number itself, say that it is a virtue. 
If B stands for a moral quality, say justice, we are not to 
be allowed to affirm of it what could not be affirmed of 
justice, say that it has four sides. The sign is still a sign, 
a sign of what it was made to stand for. 

122> Third Law. — We may demand at any time, that 
the Notion should be substituted for the Sign. As we 
are always at liberty to do so, so we should actually do so 
from time to time, in order to determine whether we are 



LANGUAGE. 85 

or are not making a proper predication. In abstruse 
discussion and in perplexing ratiocination, we are apt to 
lose sight of the signification, or at least of the precise 
signification, of the language we employ. But as we do 
so we are ever liable to make affirmations or denials 
which we should never make of the ideas denoted by the 
words. Principal Campbell inquires : " What is the 
cause that nonsense so often escapes being detected both 
by the writer and reader ? " The cause, I believe, is to be 
found mainly in this, that we are ever making assertions 
as to the sign, taking a loose view of what it signifies. 
Thus our forefathers reasoned that as money is wealth, 
so wealth might be increased by passing restrictive laws 
to keep money from leaving the country. The fallacy is 
seen at once when we properly define and studiously 
comprehend what the phrases money and wealth stand 
for. From the causes now referred to, mainly proceed 
the endless logomachies to be found in controversy of 
every kind. We shall often find that we have only to re' 
translate the word into the notion, and then compare the 
notion with the thing, to discover that the propositions 
which men utter with such gravity, or such confidence, 
are altogether meaningless, and that the sophistry which 
was deceiving us, is thus stript of its plausibilities. 
Every one will be inclined to allow that we should be 
careful to follow this rule when we are apt to run into 
extreme positions, or are penetrating into profound 
depths or vast heights. But in fact, it is equally needful 
to do so, when we are using familiar phrases, which we 
fancy we understand fully because we have been employ- 
ing them daily from our childhood. As Newton is said 
to have risen to his great discovery by narrowly inquiring 
into so commonplace a fact as the fall of an apple, so 
the detection of wide-spread fallacies and the discovery of 
important truth are ofttimes made bv instituting a sift- 



86 THE NOTION. 

ing inquiry into the real signification oi a phrase, which 
without being questioned by any one, has passed current 
from mouth to mouth for long' ages. 



Ill -CLASSES IN NATURE. 

123, These become aids and guides to the mind in its 
generalizations. I speak of them as aids, for the mind by 
its own internal power can form genera without any spe- 
cial reference to natural groupings. It must always, in- 
deed, have some supposed attribute to bind the objects 
together, and act as ground of the arrangement. But 
then it can fix on any one attribute and form a class com- 
posed of all the objects which possess it. Every thing 
may be arranged in as many classes, actual or potential, 
as it possesses qualities. The same man may, in respect 
of his country, be an Englishman or an American ; of his 
religion, a Catholic or a Protestant ; of his race, a Celt or 
a Saxon ; of his profession, a lawyer or a physician ; of his 
domestic condition a bachelor, or married ; of his politics, 
a conservatist or a liberal ; of his knowledge, a scholar or 
an ignoramus. Looking to any given company of men, 
women, and children, we might arrange them in a great 
number of ways : according to their native country or coun- 
ty ; according to their sex, age, weight, strength, mental 
capacities, education, business in life, character, creed ; 
nay, according to such insignificant qualities as the color 
of their hair or eyes, or their Christian names. Wherever, 
in short there is a property which more than one person 
possess or are supposed to possess, we have a ground 
for a classification which may be expressed by a generic 
term. The classes which man may form cannot be said 
to be infinite, but they are indefinite ; no limits can be 
pet to them. There is a manifest advantage in all this ; 



CLASSES IN NATURE. 87 

for we can arrange the objects we meet with, now in this 
way and now in that way, according to the end we have 
in view at the time. 

124:. But so far as natural and especially organic ob- 
jects are concerned, there are groupings formed which 
men should notice, and which have an existence whether 
they notice them or no. In the study of nature we are 
constantly made to feel that we have not to form or create 
classes ; the classes are already formed for us, and all we 
have to do is simply to observe them. And if we would 
construct any thing like a complete classification of natu- 
ral objects, it is imperative on us to attend to the natural 
groupings. An arrangement which overlooks this will 
turn out to be incomplete, and incapable of serving any 
practical purpose ; and however ingeniously formed will 
be characterized as artificial, even when not denounced 
as arbitrary and capricious. The Creator has so con- 
structed and disposed his works that there are facilities 
for forming classes, and it is the business of the natural- 
ist to discover and follow the natural order. So far as he 
gets hold of it his classifications will be natural, and use- 
ful for the accomplishment of an immense number and 
variety of purposes, scientific and practical. 

125. We have shown {Method of Divine Government, B. II., C. 
L, § 4, and Typical Forms and Special Ends in Creation), that there 
s an order running through all nature iu respect of such qualities 
is Number, Time, and Form. (1.) Ntcmoer. The laws of physics 
and of chemistry, etc., are expressed in quantities. The law of 
gravitation is, that all matter attracts other matter inversely ac- 
cording to the square of the distance ; and all chemical compositions 
and decompositions take place according to numerical rule. (2.) 
Time. All the leading events in the earth and heavens run in pe- 
riods : there are days and months and seasons and years, and magni 
anni. (3.) Form. The heavenly bodies have spheroidal shapes ; 
minerals crystallize geometrically with fixed angles and proportions 
and every animal and plant and every organ of the animal an<* 
plant has a typical form which it tends to assume. 



88 THE NOTION. 

126. We are thus introduced to those classes which 
have been called Kinds by some logicians. In these the 
possession of one characteristic mark is a sign of a num- 
ber of others. The botanist has seized on a classification 
of this hind. The grand division of plants is into acoty- 
ledons, monocotyledons, and dicotyledons. This is a dis- 
tinction of Kinds, and the mark fixed on becomes the sign 
of others. Thus monocotyledons grow from within and 
their leaves are parallel-veined, whereas dicotyledons 
glow from without by adding rings and have netted veins. 
In the same way in the approved classifications of zoology, 
the possession of one mark becomes a sign of others. Thus 
certain animals are called mammals because they suckle 
their young ; but all these are found besides to be warm- 
blooded, and to have four compartments in the heart. 
How different are these from artificial classes, as suppose 
we were to divide plants according to their height, or 
animals according to their color. Every one sees how 
arbitrary, in short how unnatural, such an arrangement 
would be. It would separate plants from each other 
which are most closely allied, and might put in one group 
bird and fish, man and brute, while it separated an ani- 
mal from its mate or from its offspring. 

127. " There are some classes the things contained in which 
differ from other things only in certain particulars which may be 
numbered ; while others differ in more than can be numbered, more 
even than we need ever expect to know. Some classes have little 
or nothing in common to characterize them by, except precisely 
what is connoted by the name : white things, for example, are not 
distinguished by any common properties except whiteness: or if 
they are, it is only by such as are in some way dependent upon, or 
connected with whiteness. But a hundred generations have not 
exhausted the common properties of animals or of plants, of sul- 
phur or of phosphorus ; nor do we suppose them to be exhaustible 
but proceed to new observations and experiments, in the full con 
fidence of discovering new properties which were by no means im 
Dlied in those we previously knew." " There is no impropriety iD 



CLASSES IN NATURE. 8tf 

Baying that of these two classifications, the one answers to a much 
more radical distinction in the things themselves than the other 
does, etc." (Mill's Logic, B. I., C. VII.) 

128. These groupings of nature, while they are a 
help, are at the same time a rule in the formation of 
classes. They assist, but they also control mankind in 
the construction and use of their general notions. Things 
come to be arranged by practical observation and by 
science in a certain way ; a corresponding nomenclative 
is devised, and all men must accommodate themselves to 
it. Such divisions of time as into days and years and 
seasons, of material objects into mineral, plant, and ani- 
mal, of the heavenly bodies into star, planet, comet, and 
meteor, come to be universally adopted, and all persons 
must proceed upon them ; while science is every year add- 
ing newly-discovered laws, which become known first to 
the learned and then descend as a heritage to the people. 
The concepts thus formed on distinctions in nature, have 
a reality above other concepts. Such a concept as ' white- 
colored,' has, no doubt, a sort of reality in the nature of 
things — it has a reality in the white color possessed by all 
the objects in the class, say lilies and snow. But such 
concepts as Eosacese and Cruciferse, as Crustacese and 
Foraminiferse, have a deeper signification — the class has 
a reahty in the divinely appointed order of things. It is 
the same with such generic notions as beautiful, good, 
holy — they denote primarily one quality, but they imply 
other qualities associated with it and numberless affinities. 
This was one of the truths pointed at, but never accu- 
rately expressed in, the ideal theory of Plato and the 
medieval doctrine of realism. Concepts of this descrip- 
tion have a place in the very nature of things and in theii 
ramified connections. But while this holds good of cer- 
tain concepts, it is not true of all ; and even in regard to 
those of which it is true, the reality is, after all, in the 



90 TEE NOTION. 

individual things and their mutual relations, and not in a 
mere idea in the mind of the person contemplating 
them. 



REALISM, NOMINALISM, AND CONCEPTTJALISM. 

• 

129. In the Eisagoge of Porphyry there occurs the following 
statement : " I omit to speak about genera and species as to whether 
they subsist (in the nature of things) or in mere conceptions only ; 
whether also, if subsistent, they are bodies or incorporeal, or whether 
they are separate from or in sensibles and subsist about these." 
Boethius (6th Gent) commented on this passage and declared : 
" non est dubium quin vere sint." " Stmt autem in rebus omnibus 
conglutinatae et quodam modo conjunctae atque compactae." This 
came to be the general and the orthodox opinion of the early scho- 
lastic teachers. But as curious youths mused on this cautious pas 
sage of Porphyry with the comment of Boethius upon it, we can 
conceive that some would be tempted to form an independent, 
opinion on so complicated a subject. This seems to have been the 
case with Boscellinus, a native of Brittany, who flourished in the 
eleventh century. Unfortunately we have no writings of Boscelli- 
nus, and we have to gather his opinions from the statements of his 
opponents, particularly Anselm. He is represented as maintaining 
that genera and species had no true existence — that they were no- 
thing but words {flatus vocis), and this doctrine was denounced as 
inconsistent with the higher doctrines of religion, particularly the 
doctrine of the Trinity. We have now, then, an expounder of 
Nominalism as opposed to Realism. At a little later date appeared 
the illustrious Abelard, who opposed with great acuteness the sys- 
tems both of the Realists and the Nominalists, pointing out the dif- 
ficulties in which the former are involved when they maintained 
that uuiversals are realities different from individual things, and 
showing the insufficiency of the theory of the latter. His own 
opinion is regarded by some as Conceptualisin — it is at least an 
anticipation of Conceptualisin. The following is M. Cousin's ac- 
count of it : " There exists nothing but individuals, but none of 
these individuals is, in itself, either genus or species, but the indi 
viduals have resemblances which the mind can perceive, and these 



iWALISM, NOMINALISM, ETG. 91 

resemblances considered alone and abstraction being made of theii 
differences, form classes more or less coinprehensive which they call 
genus or species. Species and genus are then the real products ol 
the mind ; and they are not words, although words express them ; 
nor are they things without or within the individuals — they are con- 
ceptions. Hence the intermediate system named Conceptualism." 
(Fragmens). We have now the three possible systems contending 
with each other. Realism was the~prevailing doctrine throughout 
the Middle Ages, and was defended with great zeal and ability by 
Albert of Cologne (Albertus Magnus), and Thomas Aquinas {Doctor 
Angelicus). Opposed to Thomas the Dominican was John Duns 
Scotus (Doctor SubtUis) the Franciscan. Like Thomas be was a 
Realist, but he maintained that the universal existed in individuals 
not really, but formally (formaliter). William Occam (Doctor I/i- 
wncibilis) a disciple of Scotus, is usually regarded as a Nominalist, 
but Dr. Mansel declares that he is a Conceptualist like Abelard. In 
modern times it is difficult to find a genuine Realist, but we have 
one in Harris, the author of Hermes. Adhering to the Nominalist 
theory we have Hobbes, Berkeley, Hume and Whately ; and among 
numerous Conceptualists we may mention Locke, Reid, Kant, Brown, 
and Whewell. 

l.'iO. The controversy has been characterized throughout by 
great confusion of thought. The extensive survey we have taken of 
the Notion and of Language should enable us to discover the truth 
and the error in each of the systems. 

Realism errs by excess. It errs when it ascribes to the universal 
an existence independent of singulars or distinct from them. Plato 
held that Ideas had an existence in or before the Divine Mind from 
all eternity. He was met by Aristotle, who showed that they had 
no existence except in the individuals. The medieval doctrine of 
the reality in universals was a modification of the Platonic doc- 
trine. In both there is a tendency to mysticism, and a disposition 
to hypostasize the conceptions of the mind. Yet the system has no- 
ticed certain important truths. First the mind has a tendency to 
rise beyond the particular to the general, and to reduce multiplicity 
to unity. Then all organisms, all plants and animals, tend to as- 
sume a typical form. The individuals all die, showing how perishing 
they are, but the genus and species survive. The flowers of last 
summer are all faded, but in the coming summer flowers of the same 
form will spring up. Then all the powers of nature act according 
to laws imposed on them, and amidst the flux of things these laws 



92 THE NOTION. 

are permanent. Still more important, we find, amidst the impel 
tectums and sins of humanity, the moral law of God abideth for- 
ever. 

131. Nominalism errs by defect. It forgets that there must be 
grouping of objects by the mind in order to the introduction of a 
common term, and an apprehension of the grouping in order to an 
intelligent use of the term. It forgets that the mind can form an 
image of a class of objects, inadequate, but still sufficient in most 
cases to enable it to think about them. It overlooks the important 
circumstance that in nature there are laws and types ordained by 
the Being who formed the objects themselves. The truth contained 
in nominalism is, that words greatly aid the mind in thinking, and 
enable it to conduct its cogitations much farther than it otherwise 
could. 

132. Goneeptualism has often taken a wrong form. It does so 
when it regards the conception combining the objects as an idea in 
the sense of image. This was the mistake of Locke, when he says 
that in forming our idea of man we leave out of the complex idea 
that which is peculiar to each of the individuals, and retain only what 
is common to all. (See §79.) Again it errs when it overlooks or 
denies the utility, in some cases the necessity, of signs to enable us 
to conduct our thinking. And Conceptualists have often, in looking 
at the idea, forgot that there is an actual order among the things 
on which the idea is founded. But if it avoids these mistakes and 
oversights, which are not parts of the doctrine properly understood, 
conceptualisin is the true theory. For in general notions, the essen- 
tial element is the grouping by the mind of objects by common 
properties, and putting in the group all objects possessing the 
properties. 

There are universalia ante rem in the Divine Mind. There are uni- 
versalia in re in Natural Classes. There are universalia post rem in 
human concepts and terms. 



PART SECOND. 
JUDGMENT. 



1. Judgment is defined by logicians " as the comparing 
together in the mind two of the notions or ideas which are 
the objects of apprehension, and pronouncing that they 
agree or disagree." But this definition can be accepted 
only when we understand by notions, not mental states 
as such, but objects apprehended. When we say " Alex- 
ander the Great was ambitious," we are comparing 
" Alexander the Great " and " ambitious," and not mere 
ideas of the mind — it being always presupposed that the 
objects are previously apprehended by us. A Proposition 
is a Judgment expressed in words, and in it we compare 
two Terms, so called because they are the termini (boun 
daries) of the proposition. 

CATEGORICAL PROPOSITIONS. 

2. Judgment is psychologically one act of the mind, 
but is of a concrete nature, and we analyze it into three 
elements, two notions, and the declaration of their agree- 
ment or disagreement. That notion which we seek pri- 
marily to compare is called the Subject ; that with which 
we compare it, the Predicate ; and the determination oi 
the agreement or disagreement, the Copula. The Judg- 



94 JUDGMENT. 

ment may be expressed in three words, or in a number oi 
words, or even in one word. When we say " selfishness 
is hateful," we bave subject, copula, and predicate, each 
in one word. But there are tongues in which the judg 
ment can be expressed in one word, as amat ; which, when 
we wish to bring out each of the parts we analyze and 
say, itte est amans, he is loving. Active verbs in a sen- 
tence commonly express both copula and predicate ; 
thus, when we say " the horse neighs," the word ' neighs ' 
contains both predicate and predication, and when ex- 
panded takes the form " the horse is neighing." In order 
to determine what are the terms, we must look, not to 
the mere words, which may differ in different languages 
and even in the same language in expressing the same 
idea, but to the notions. When it is said that " it is a 
true saying and worthy of all acceptation, that Jesus 
Christ came into the world to save sinners," the two 
terms, as ascertained from the two notions, are " Jesus 
Christ coming into the world to save sinners " and " a 
true saying and worthy of all acceptation ; " these are the 
things compared in the mind, and in respect of which we 
predicate their agreement. 

3, The copula is usually expressed by logicians by the 
present tense of the verb ' to be,' by ' is,' or ' is not,' (or 
' are ' and ' are not.') But we are not to understand ' is ' in 
such a connection, as being the substantive verb — the sub- 
stantive verb in the Latin form, est, contains subject, 
copula, and predicate, meaning "he is existing." The 
copula is an abstract, expressing neither less nor more than 
the agreement or disagreement. Every thing else in a 
proposition is to be regarded as part of the subject or of 
the predicate. The element of time, when it is involved 
in a judgment, is not to be attached to the copula. When 
we say " Napoleon Bonaparte was unfortunate in 1815," 
the notions compared are "Napoleon in 1815 " and "un- 



CATEGORICAL PROPOSITIONS. 95 

fortunate/' and it is on comparing these that we declare 
their agreement ; if we were speaking of " Napoleon in 
L808," we should have to declare that it disagreed with 
" unfortunate." 

4:. It is thus that most logicians do now dispose of what are 
called Modals, that is, propositions in which we make a predication, 
not absolutely, but after a mode. Thus, when it is said that " Bru- 
tus killed Caasar justly," we are not to understand the predicate as 
being " the killer of Caesar," but " the just killer of Caesar." 

Sm The Quality {iroiorriq) of a proposition, that which 
makes it to be a proposition or a judgment, is its predica- 
tion, its affirming or denying an agreement or disagree- 
ment between the terms. In respect of Quality, all prop- 
ositions are either Affirmative or Negative — they either 
affirm or deny the agreement of the subject and predicate. 

0. The predicate may be affirmed or denied either of 
the whole or part of the subject. When it is predicated 
of the whole, the proposition is said to be Universal ; 
when not of the whole, it is said to be Particular (ei> iiepei,). 
This division of propositions is said to be made in respect 
of their Quantity, that is, the extent of the predica- 
tion. "When it is said "all poets are men of genius," 
the proposition is universal, the affirmation is made of all 
poets. When it is said " some poets have not common 
sense," the assertion is made only of a part of the class. 
Such phrases as " every one " and " all " in affirmative 
propositions, and " no," " no one," and " none " in nega- 
tive propositions, are the signs of universality. The sign 
of particularity is " some " in the sense of " some at least," 
— we may not know how much or how many., 

7. The word " all " is ambiguous. It may mean " every one," 
every one of a class, as when we say " all books are meant to be 
read." It may also mean all collectively, meaning the whole class, 
as " all the books constitute the library." In this latter sense, the 
term is singular-abstract. (See §48). In both senses the proposi 
tion is reckoned Universal. The word " some " is also ambiguous 



96 JUDGMENT. 

It may signify " some, not all," "some at most ; " as when we say 
" some lawyers are not greedy," implying that there are some 
who are. It may mean " some-certain," as when it is said that 
" some sciences are classificatory," pointing to mineralogy, botany, 
and zoology. In Logic " some," as the sign of particularity, signi 
fies " some at least ; " it may be only one, or it may even be all, 
provided we do not declare it to be all. 

8* In order to determine the quantity of a proposition; 
we must look, it is evident, to the subject. In many sen 
tences the quantity is not indicated by the language, but 
v it must always be understood in thought. When it is 
said that " men have the power of speech," we mean " all 
men," and not merely " some men." But when it is said 
that " books are necessary to a library," we mean not " al] 
books," but " some books." Terms in which the quantity 
is not indicated by the language are called " indefinite " 
or " indesignate " (Hamilton). 

0, Combining these cross-divisions, we have a fourfold 
division of propositions : 

Universal Affirmative denoted by A. 
Universal Negative " E. 

Particular Affirmative I. 

Particular Negative " 0. 

Asserit A, negat E, verum generaliter ambo. 
Asserit I, negat 0, sed particulariter ambo. 

' 1ft. This may be the proper place for explaining what 
is meant by the Distribution of Terms in a proposition. 
A term is said to be distributed when it is used for all its 
significates. When it is said " reptiles are cold-blooded," 
the general term " reptiles " is distributed — it includes all 
and every reptile. But when it is said that " food is 
necessary to life," the general term "food" is not dis- 
tributed, for it does not mean every kind of food, but 
food of some kind. Singular Terms and Abstracts are 
always to be reckoned as distributed. When it is said 



CATEGORICAL PROPOSITIONS. 97 

Shakespeare is the greatest poet that ever lived," 
Shakespeare is to be taken for the man, for the man as 
a whole — we do not make the affirmation of some Shake- 
speare, or Shakespeare in part ; and the proposition is 
regarded as universal, A„ by logicians. It is the same 
with abstracts proper, as "pride goeth before destruc- 
tion," meaning, not " some pride," but the one thing 
" pride." It is always to be kept in mind, indeed, that 
abstracts may become common terms (see § 49), as when 
we talk of various kinds of pride, as pride of intellect, 
pride of life ; in such we are to ascertain whether the 
term is distributed or not, as we do in the case of any 
other general term. 

11. From the account now given, it is clear that in all 
Universal propositions, A and E, the Subject is distribu- 
ted, and that in all particular propositions, I and O, it is 
undistributed. As to the Predicate, it is to be regarded 
as distributed in all negative propositions. When we 
say " no brute is immortal," " some men are not misers," 
we exclude brutes from the whole class of immortals, and 
certain men from the whole class of misers. When the 
Predicate is a general notion, it is not to be understood 
as distributed in affirmative propositions. When it is 
said that " men are mortal," the term mortal is not taken 
for all its significates ; we cannot say " all mortals are 
men." But it is of importance to remark (the signifi- 
cance of it will come out as we advance) that as singular 
and abstract terms are distributed and regarded as uni- 
versals, so the predicates which are formed by such are 
always to be regarded as distributed. In the proposi- 
tions " Homer was the author of the Iliad " and the 
" Uiad was the greatest of Greek poems," the terms 
"author of the Iliad," and "the greatest of Greek 
poems," are taken in all their extent. 

12. The question is much discussed, what are the re- 

7 



98 JUDGMENT. 

lations between the objects compared in a judgment. 
The proper answer is that they may be as many and va- 
ried as the relations which can be discovered between 
things by the mind of man. What is the number and 
what the nature of these relations, is a question to be 
settled — if it can be settled — by physics or metaphysics, 
and not by logic. The varied relations are all involved 
in those acts in which we compare single objects with 
each other. Judgments in regard to individual things 
must evidently be the first formed by the mind — they 
must precede the formation of concepts, for it is by re- 
semblance between individuals in respect of some quality 
that we are able to gather them into classes. Sfcich judg- 
ments have been called Psychological by Dr. Mansel, to 
distinguish them from Logical. For logical purposes, 
that is in the discursive comparison of notions, judg- 
ments may be regarded as of two kinds. 

13. N.B. The relations which the mind can discover have heen 
variously classified by philosophers. In the Intuitions of the Mind, 
(P. II., b. iii.), the human intellect is represented as capable of per- 
ceiving the relations of (1) Identity, that is, that the same is the 
same observed at different times and in different circumstances ; (2) 
Whole and Parts (Comprehension, Abstraction, Analysis, Synthesis) ; 
(3) Space (Extension, Figure) ; (4) Time ; (5) Quantity (Less or More) ; 
(G) Resemblance ( Classification) ; (7) Active Property ; (8) Cause and 
Effect. These may all be noticed in the relation of individual 
things. But for logical ends the relations may be considered as 
two. 

14. First. There are Equivalent Propositions, or 
Equipollent Propositions — to use a phrase of the old lo- 
gicians somewhat modified. Here the agreement of the 
terms is one of identity or equality. In all such the sub- 
ject may take the place of the predicate, and the predi 
cate the place of the subject without any change. Under 
this head should be placed all those cases in which both 
the notions compared are Singulars or Abstracts, as 

' Milton was the author of Paradise Lost," " Bomulus 



CATEGORICAL PROPOSITIONS. 99 

was the founder of Rome." These propositions being 
given, we can say " The author of Paradise Lost was 
Milton," " The founder of Rome was Romulus." To this 
class belong arithmetical and geometrical propositions as 
3 + 3=6. Here the terms are abstracts, and we can say 
6 = 3 + 3. It is of importance to observe that to this 
class belong all definitions, as "Logic is the science of 
the laws of discursive thought," Natural History is the 
science of the classification of animals and plants." In 
these propositions the terms are Abstracts, neither Per- 
cepts on the one hand, nor Concepts on the other ; and 
we can convert simply, and say " the science of the Laws 
of discursive thought is Logic " and " the science of the 
laws of the classification of animals and plants is Natural 
History." (See P. I., § 73.) In all such, neither term has 
any claim in itself to be regarded as subject or as predi- 
cate. That is the subject which is primarily before the 
mind of the speaker to be compared with something else, 
and that is the predicate with which it is compared ; and 
the speaker or writer may have either term primarily in 
his thoughts, or now he may have one and now the 
other. 

15. Second. There are propositions in which the 
agreement is one of joint Comprehension and Extension. 
In all such it will be found that one of the notions is a 
concept, or that both are so. Take the proposition 
" Longfellow is a poet." Here the subject is a Percept, 
and the predicate a Concept. The proposition may be 
interpreted in one or other of two ways : in Comprehen- 
sion, meaning that "Longfellow has the attribute of 
writing poetry ; " or in Extension, meaning that "he is in 
the class of poets." Or we may take a case in which both 
terms are Concepts, as " Crocodiles are reptiles ; " which 
may be interpreted " the class crocodiles possess the at- 
tributes of reptiles ; " or, " the class crocodiles are in the 



100 JUDGMENT. 

class reptiles." It has often been disputed whether prop- 
ositions are to be understood in Comprehension or Ex- 
tension. The proper account is that in those we are now 
speaking of they are to be understood in both. I be- 
lieve, indeed, that in the greater number of propositions, 
in particular in all propositions in which the predicate is 
a verb, the uppermost thought is in Comprehension : 
when we say " men think," we mean that they are in 
the exercise of thinking. But as an attribute possessed 
by objects maj always be a bond to unite them into a 
class, so we may interpret the proposition in Extension 
also, and say "men are among the class of thinking 
beings." And in many propositions the uppermost 
thought is in Extension. When we say " the crocodile is 
a reptile," our primary intention may be to indicate 
that it is in the class. But as Extension always implies 
Comprehension, that is, a class always implies a quality 
to bring the objects into the unity of a concept, so we 
may always interpret the proposition in Comprehension 
likewise, and say " the crocodile has the attributes of 
reptiles." 

16, The distinction between these two classes is of 
great logical importance. It was noticed by Aristotle 
who divided propositions into Convertible and Uncon- 
vertible, and appears in the present day in the distinction 
drawn by Archbishop Thomson between Substitutive and 
Attributive Judgments. We have seen that in the former 
class we can at once put the subject in the place of the 
predicate, and the predicate in the room of the subject. 
In the other we cannot do so without changing the predi- 
cate ; thus in the Attributive Judgment " all men think," 
we cannot convert simply, and affirm "all thinking beings 
are men." It has not been noticed that in the first class 
both notions are Percepts or Abstracts, and that in the 
second the predicate is a Concept. 



CATEGORICAL PROPOSITIONS. 101 

17. In the second class there is a real difference be- 
tween the subject and the predicate, whereby the one 
comes primarily and the other secondarily in the order of 
thought. We may say for poetical effect " sweet is the 
breath of morn," but the natural order in thought is 
" the breath of morn is sweet." The rationale is, that in 
predication we ascribe an attribute to an object, or we 
place it in a class ; and in both the predicate must be 
more extensive and less comprehensive than the subject. 
This is the the rule at least for affirmative propositions, 
that the subject is the more comprehensive and less ex- 
tensive. 

18. Certain negative propositions seem to be exceptions. Thus 
when we say " all Greeks were not Athenians," the subject is more 
extensive than the predicate. But the proposition is not a univei-' 
sal negative, E : we do not say of every one of the Greeks that they 
were not Athenians, or that no Greek was an Athenian ; but that 
" some Greeks were not Athenians." But then even in this form the 
subject is the more extensive. But is not the proposition in thought 
" some Greeks were Not-Athenians," in which we constitute a clasB 
of all persons Not-Athenians, which is more extensive than Greeks ? 

10. It is disputed what we are to make of those prop- 
ositions in which the predicate is a general notion dis- 
tributed, e. g., "all men are all rational beings." It is 
clear that when we say simply " all men are rational," we 
mean that every one man, every one in the class man, is 
in the class rational. But if we have farther found that 
every rational being is in the class man, we are entitled 
to say '•' all men are all rational." But what do we mean 
when we say so ? The terms, it appears to us, are no 
longer general, standing for each and every one of a class ; 
we do not mean " every one man = all rational," nor 
" every one man = every rational." The word " all " 
does not now mean " every one," but the whole collec- 
tively (see § 48). The meaning in fact now is, " the 
whole class men — the whole class rational." If so, the 



102 JUDGMENT. 

terms are not General, applicable to each and every one 
of an indefinite number, bat Singular, with a process of 
Abstraction involved. To take one other example. The 
mathematician demonstrates that " equilateral triangles 
are equiangular," meaning that every one equilateral tri- 
angle is so. He also demonstrates that " equiangular tri- 
angles are equilateral." He can now say "the whole 
class of equilateral triangles is equal in extent to the 
whole class of equiangular," and the terms are Singular 
Abstracts, and the propositions Convertible, Substitutive, 
Equivalent or Equipollent. 

20. We have called attention (§ 9) to the fourfold 
division of propositions A, E, I, O. But we have now 
seen that there is a class of Universal Affirmative prop- 
ositions in which the predicate is distributed. To dis- 
tinguish them from A, in which the predicate is not dis- 
tributed, it is proposed to designate them by the vowel 
U (Hamilton), or A 2 (Spalding), which would represent 
that class of propositions in which the terms are Sin- 
gulars or Abstracts, and Convertible. 

21. According to Aristotle, every proposition declares a genus 
(vevoc), or a property (L5lov), or a definition (<5pof), or accident (av/nj3e 
8?]k6(), of the subject. Genus denotes a part or attribute belonging 
to the subject, but also to other subjects, as " mammals are verte- 
brates," where the predicate applies to other subjects as well. A 
property belongs invariably to the subject, but without being the 
mark which explains its nature, as that "mammals are warm- 
blooded." Definition is an attribute or set of attributes explaining 
the very nature of the subject, as that mammals suckle their young. 
Accident is an attribute belonging to the subject, but which might 
be conceivably separated from it, as that mammals are found in 
America. This makes the predicables four in number. Porphyry 
has five Predicables, genus, species, proprium, differentia, and acci 
dent, leaving out definition and adding species (tvJof) and differentia 
(diafopu). Species is the whole essence of its subject. Differentia 
is that attribute or set of attributes by which a species is distin 
guished from other species of its genus. 



CATEGORICAL PROPOSITIONS. 103 

Some of these distinctions are of great importance, as that be- 
tween genus and species (P. I., § 35) ; and that between definition 
and proprium, or, as Porphyry makes it, between differentia and 
proprium. In species and differentia, e. g., " mammals suckle their 
young," the subject and predicate are convertible or equivalent or 
coextensive. In proprium, e. g., that " mammals are warm-blooded," 
the terms are not convertible, for there are warm-blooded animals 
which are not mammals. The distinction between differentia and 
proprium is valuable as showing that when we have fixed on the 
differentia of a class, we may often find other attributes conjoined 
with it which may be called propria. This is the case with those 
classes which are called Kinds (Part I., § 126). It is difficult, how- 
ever, in some circumstances, to determine what is differentia and 
what is property. Under one view, that is, to the sailor, polarity 
would be the differentia of the magnet, while under another aspect, 
" to those manufacturers who employ magnets for the purpose of more 
expeditiously picking up small bits of iron and for shielding their 
faces from the noxious steel-dust in the grinding of needles, the at- 
tracting power of the magnet is the essential point." (Whately.) It is 
extremely difficult to carry out these distinctions thoroughly and con- 
sistently. We cannot tell what is the whole essence of any subject ; 
all that we can do is to specify one or more of the determining attri- 
butes of a species. Nor can we say in all circumstances what is an 
accident as distinguished from a property, say, e. g., whether that it 
lives on the earth is the property or accident of a mammal. The 
distinction adopted in the text between Equivalent propositions in 
which the terms are coextensive and interchangeable, and Attribu- 
tive propositions in which the relation is one of joint comprehension 
and extension and in which the predicate is undistributed, seems to 
be the important one for logical ends. 

22. Hamilton maintains that the predicate should always b© 
quantified, that is, declared to be either particular or universal ; that 
we should say logically, " all men = some fallible." He argues this 
on the ground that whatever is contained implicitly in spontaneous 
thought should be unfolded explicitly in logical forms. We admit 
the principle, but we deny that it requires the quantification of the 
predicate in affirmative propositions. In the great majority of 
affirmative propositions, the predication is made in comprehension 
rather than extension. When we say " the bird sings," we are at- 
tributing a quality to the bird, and we are not determining in 
thought whether there are or are not other creatures that sing 



104 JUDGMENT. 

When we say " man reasons," we are ascribing a property to him 
probably without settling whether there are or are not other beings 
who reason ; and so the logician is not required to put the proposi- 
tion either in the form "all men = some reasoning beings," or " all 
men = all reasoning beings." And this may be the proper place 
for stating that there is no appropriateness in using the sign of 
equality, =, which has a definite meaning in mathematics, to ex- 
press the connection of the notions in attributive propositions in 
which the relation is one of comprehension and extension and not 
jf mere equality. 

23. Carrying out his doctrine of the thorough quantification ol 
the predicate in all propositions, Sir W. Hamilton gives the follow- 
ing Table of Judgments : 

A All plants grow. 

E No right action is inexpedient. 

I Some muscles are without our volition. 

O Some plants do not grow in the tropics. 

IT Common salt is chloride of sodium. 

T Some stars are all the planets. 

j) No Frenchman is some German. 

u Some trees (oaks) are not some trees (elms). 
The two marked by the Greek letters are criticised by Thomson and 
rejected on the ground that while they are conceivable cases of neg- 
ative predication they are not actual — we woidd add in spontaneous 
thought. Thus rj has the resemblance, not the power of denial ; it 
denies nothing, and decides nothing. T should also be discarded on 
the ground that it is never uttered by us in spontaneous thought, in 
which we say instead " all the planets are stars," which is A. Kejecting 
these three forms on these special grounds, we farther decline to give 
them a separate place in the Table of Judgments, on the general 
ground that in spontaneous thought the predicate is not quantified 
in all or even in most judgments. We admit that they are forms 
which may be reached by Conversion or other kinds of Immediate 
Inference to be explained forthwith ; but then it has never been 
deemed necessary or even proper to introduce such among the forms 
of spontaneous j udgment ; and if we adopt these we must by parity 
of reason introduce others, and make the Table contain many more 
judgments. We are inclined, however, to think that it is of im- 
portance to separate those propositions which are Equivalent from 
others, and to have a letter, U, to designate them. But let it be 
observed that in the Judgments thus denoted, the notions compared 



CONJUNCTION OF PROPOSITIONS. 106 

are Percepts or Abstracts. We are thus enabled to retain the old 
Table, A, E, I, 0, for all those judgments in which we have a Con- 
cept, while U is added to designate that class of propositions which 
have been seen to be Convertible since the days of Aristotle, and 
which turn out to be those in which the notions compared are not 
general or class notions. 



CONJUNCTIONS OF PROPOSITIONS, CONDITIONALS, AND 
DISJUNCTIVES. 



24:. We have now to consider propositions in their 
relations one to another. Most of these relations are of 
so loose a nature that they cannot be brought under any 
laws of discursive thought. When we say " the road was 
long and steep," we have two propositions, " the road was 
long " and " the road was steep," but with no special con- 
nection except that in both the affirmation is made of 
" road." When we say that " the fever was virulent, but 
the patient recovered," we have two affirmations so far in 
a state of opposition, but not involving any discursive pro- 
cess falling under Logic. Such connections of sentences 
are indicated by connective particles, such as " and," 
" but," " then," " afterwards," " either," " neither," " so," 
" however," and attempts have been made by gramma- 
rians, with only imperfect success, to classify them into 
conjunctive, adversative, &c. 

25. But propositions may be so connected as to in- 
volve a discursive process falling under the laws of 
thought. We do not refer now to that formal conjunc- 
tion of propositions which forms reasoning, but to the 
tin-owing of two or more connected propositions into one. 
The propositions hitherto considered are called Categor- 
ical, in which one proposition is simply said to agree or not 
to agree with another. But there are propositions in which 
the predication is made hypothetically, and which are 



106 JUDGMENT. 

therefore called Hypothetical. They are of two kinds, one 
called Conditionals, the other Disjunctives. 

26» There are Conditionals or Conjunctives in which 
the predication is made under a condition. "If the night 
continues clear there will be dew on the grass." Here we 
have two categorical propositions, " the night is clear " 
and " dew will be on the grass, 5 ' and we put them into one 
proposition, which affirms that they are so related that the 
one depends on the other. It is certainly desirable in every 
way to have the propositions spread out and then- connec- 
tion intimated in the conditional form, as it is only thus we 
can perceive fully the relations of things and of thoughts. 
But it is of equal importance that we should be able to 
detect the one proposition in the affirmation that they 
agree, and that we should be able to point out its subject, 
its predicate, and copula. 

27. The proposition on which the other depends, wheth- 
er placed first or last, is called the Antecedent, that which 
depends on it the Consequent, and the relation between 
them the Consequence. Sometimes there are four terms 
in the Conditional. " If the sun attracts in the same line 
as the moon, the tides are at the highest." Here we have 
four terms ; " sun," " attracting in the same line as the 
moon," "tides," "at the highest." But in propositions 
with such a connection it will often happen that the same 
term appears both in the antecedent and consequent, 
either as subject or as predicate. " If the man pursues 
an honest course he will prosper." " If virtue is volun- 
tary, vice is voluntary." In all cases the two propositions 
are put into one in the Conditional, and we have to find 
the one subject and the one predicate in the affirmation. 
" The night continuing clear," subject ; " will have dew 
on the grass," predicate. " The sun attracting in the 
same line as the moon," subject ; " will have tides at the 
highest," predicate. All Conditional Propositions are to 



CONJUNCTION OF PROPOSITIONb 10? 

be regarded as affirmative. Even when we say that " ii 
the night becomes cloudy there will be no dew," the prop- 
osition is not to be regarded as negative, for what we 
affirm is a relation between the cloudiness of the night 
and the absence of dew. 

28. The logician does not require to consider what is the nature 
of the dependence of the consequent on the antecedent, whether 
it is in things or in thought, whether it is or is not the relation ol 
;ause and effect, or whether the relation of cause and effect is neces- 
sary or contingent. He leaves all these questions to the physical 
investigator or the metaphysician. To him the relation of the two 
propositions is given, aud he has to consider the discursive thought 
involved in the relation of the two propositions. 

29. Conditional propositions may be Equivalent or 
they may be Attributive, and we are to determine to which 
class they belong, in the same way as we do in Categori- 
cals. The examples given above are all of Attributives. 
But when the terms are singular and abstract, we shall 
have Equivalent Conditionals, e. g., " If the relation be as 
4 to 16, it is the same as that of 1 to 4," or, in Categorical 
form, " the relation of 4 to 16 is the same as the relation 
of 1 to 4." 

30. Disjunctive Propositions express the relation of 
two or more judgments which cannot all be true, but one 
or more of which must. It involves two or more judg- 
ments brought into one. It jxroceeds on the principle of 
Logical Division (Part I., § 58), implying that we have 
divided a genus into its co-ordinate species. "Judgment" 
is the genus, and we find in respect of quality that " every 
judgment is affirmative or negative." Here we have two 
members in two propositions, " every judgment affirms," 
" every judgment denies," and we declare that " everv 
judgment either affirms or denies." These cannot both 
be true, but one or other must, on the supposition that 
our division of the species is adequate to the genus. In 
the same way we may have three members, as " all notions 



108 JUDGMENT. 

are Percepts, or Abstracts, or Concepts." Or we may havo 
four members, as when we say that in respect both of 
quantity and quality, every proposition is A, or E, or I, or 
; or we may have live members if we add U, and say 
" all propositions are A, E, I, 0, or U." 

31* All Disjunctive Propositions are Equivalent or 
Substitutive. The predicates in the above examples, 
" either affirms or denies," " Percepts, Abstracts, or Con- 
cepts," " A, E, I, and 0," are not general notions embrac- 
ing an indefinite number of individuals, but abstract no- 
tions to be taken in their full extent. 



IMPLIED JUDGMENTS, OR IMMEDIATE INFERENCES. 

32. From any given proposition certain others can be 
drawn discursively by processes which the logician can 
analyze and express. These have been called Syllogisms 
of the Understanding by Kant, to distinguish them from 
Syllogisms of Seasoning. Some British writers call them 
Immediate Inferences, as distinguished from Mediate In- 
ferences, or reasoning by means of a middle term. We 
are inclined to designate them Implied or Transposed 
Judgments. They all flow from the nature of the Notion 
as above unfolded, from its interpretation, comprehension, 
extension and denomination, and from the relation of the 
notions in the jn'oposition. 

33, CONVERSION. In this process the terms are 
transposed so that the subject becomes the predicate, and 
the predicate the subject. In order to its validity, the 
truth of the converse must be implied in the truth of the 
exposita or proposition given. The main rule for secur 
ing this is, that no term is to be distributed in the con- 
verse which was not distributed in the exposita. It 
may be effected in two or three ways. (1) Simple Conver 



IMPLIED JUDGMENTS. 109 

sion, in which the terms are transposed without any change 
of quantity. This can be done in propositions in E, 
in which both terms are distributed, and in I, in which 
neither is, as E "No man is perfect," converted "No per- 
fect being is man ; " I " Some men are generous," con- 
verted " Some generous beings are men." (2) Conver- 
sion by Limitation or per accidens, by changing the 
quantity. It being given that " all deception is mean," we 
cannot say " all mean things are deception," but " mean " 
being undistributed in the exposita, we give it the sign 
of particularity or non-distribution in the converse, 
and say, " Some mean thing (or among mean things) is 
deception." A can be converted in this way, as may also 
E. (3) It is disputed whether O can be legitimately con- 
verted. " Some students are not industrious." We can- 
not, therefore, say " some industrious are not students," 
for you would have students limited in the original prop- 
osition and distributed in the converse. Some logicians 
think that conversion may be accomplished by what is 
called Contraposition, that is, by attaching the negative 
to the predicate and reckoning the proposition affirmative, 
thus making the predicate undistributed. "Some stu- 
dents are not-industrious," converted " some not-indus- 
trious are students." This is certainly a legitimate dis- 
cursive process, but seems to imply Privative Conceptions 
(see infra, § 49). 

34. OPPOSITION. Light is often thrown on the 
nature of a proposition by its being put in the various 
forms of what is called Opposition. In Equivalent prop- 
ositions there is, properly speaking, only one kind of 
Opposition, that between an affirmative and negative 
proposition with the same terms. " Common salt is 
chloride of sodium," its opposite is " common salt is not 
chloride of sodium." This Opposition is Contradictory : 
that is, both propositions cannot be true ; and yet one o> 



110 



JUDGMENT. 



other must be ; and the truth of the one implies the false- 
hood of the other, and the falsehood of the one the truth 
of the other. 

35. But when we have Concepts in the proposition, 
then the forms of Opposition become more varied. They 
are exhibited in the following diagram. 



Fvery man has a conscience 



Home men have a conscience. 




No man has a conscience 



men have not a conscience 



Subalternation, or the relation between two propositions 
which with the same terms differ in quantity, the one 
being universal and the other particular. It holds be- 
tween A and I, between E and 0. It can scarcely be 
said to be a form of Opposition. The rule is, that the 
truth of the universal implies the truth of the particular. 
If it be true that " all men have a conscience," it follows 
that " some men have a conscience." If it be that " no 
man is free from sin," it is also that " some men are not 
free from sin." From the falsehood of I we can argue the 
falsehood of A, and from the falsehood of O the falsehood 
of E. It is evident that we cannot reversely argue the 
truth of the universal from the truth of the particular, 
that we cannot argue A from I or E from O. 

36. Subalternation depends on the principle that 
whatever is true of a class, is true of any and of each of 
the members of the class. We are now on the very verge 
of Mediate Reasoning. In Subalternation we say "ah 



IMPLIED JUDGMENTS. HI 

bodies attract each other " (A), and so " some bodies 
attract each other." In Mediate Seasoning we introduce 
a third term and declare, on the same general principle, 
that "the planets, being bodies (some bodies), attract 
each other," (see Pakt Third.) 

37. Contrary Opposition, in which the propositions, 
always having the same terms, differ in Quality. It holds 
between A and E. Contraries cannot both be true. If all 
men are liars, that is, included in the class liars, it cannot 
be true that no men are liars. But they may both be 
false, that is, it may not be true either that " all men are 
liars," or that " no men are liars." The Opposition be-- 
tween I and is called Sub-Contrary. They may both 
be true but cannot both be false. Thus it is true that 
" some men are liars " and that " some men are not liars." 
But if it be false, that " some men are sinless," it must be 
true that " some men are not sinless," and if it be false 
that " some men have not a conscience," it must be true 
that " some men have a conscience." 

So it is usually said. But it should be observed that in the twc 
last instances we use " some," not in the proper logical sense 01 
' some at least," " some, we know not how many," but in another 
^ense, " some at most," " some, not all." (See § 7.) 

38. Contradictory Opposition, in which the propositions 
differ both in quantity and quality, as A and 0, E and I. 
From the truth of a proposition we can posit the false- 
hood of its contradictory. If it be true that " all men 
have a conscience " (A), it cannot be that " some men 
have not a conscience " (0) ; and if " some men have not 
a conscience " (0), it cannot be that all men have a eon- 
science (A). If "no man has a conscience" (E), it can- 
not be that " some men have a conscience " (I) ; and if 
"some men have a conscience" (I), it cannot be that 
" no man has a conscience " (E). When two prop- 
ositions are in the relation of contradictories, the truth 



112 JUDGMENT. 

>f the one implies the falsehood of the other, and 
the falsehood of the one the truth of the other. This is 
the Law of Contradiction, or, as it is called by Hamilton, 
of Non-Contradiction. But there is another law involved 
called the Law of Excluded Middle, — that of two contra- 
dictories one or other must be true, there is no Middle 
between. It must either be that " all men have a con- 
science " (A), or that " some men have not a conscience " 
(O) ; that "no man has a conscience " (E), or that "some 
men have a conscience " (I). It follows that if you prove 
the truth of a proposition, you thereby prove the false- 
hood of its contradictory ; or if you prove the falsehood 
of a proposition, you establish the truth of its contradic- 
tory. If you prove that some doctrines, such as the con- 
nection of mind and body, are to be believed, though they 
are not comprehensible, you have thereby shown that a 
doctrine is not to be disbelieved because it is incompre- 
hensible. 

30. Demonstration, that is, the establishment of a 
point by a pure discursive process founded on truth al- 
lowed, is of two kinds, direct and indirect. When the 
proposition is established by proving its truth, it is said 
to be direct. We should use this method, as being the 
most satisfactory, whenever it is available. But there is 
another mode called indirect which is also valid. You 
may prove not that a proposition is true, but that its con- 
tradictory must be false, which implies the truth of the 
proposition of which it is the contradictory opposite. 
Euclid often employs this method of demonstration, 
showing that you contradict a conceded truth by follow- 
ing any other supposition than that which he makes. We 
shall see that the same mode is employed in Logic in 
establishing the Special Rules of the Figures and in cer- 
tain forms of Reduction, 

4:0. It is desirable in controversy to have the prop- 



IMPLIED JUDGMENTS 113 

ositious defended, put in the form not of contrary but ol 
contradictory opposition. Without this the combatants 
may fight without ever facing each other, and the whole 
discussion will be characterized by hopeless confusion. 
One asserts that men may be trusted, another that men 
may not be trusted, and the contest may go on forever 
with abundant evidence on both sides ; but let the posi- 
tions assume the form " all men are to be trusted " and 
" some men are not to be trusted," and the question may be 
settled. One holds that such branches as history and meta- 
physics should be studied, another that they should not, 
and both are right and both are wrong ; but let the state- 
ments be, on the one hand, that " no history is to be stud- 
ied," or that "no metaphysics are to be studied," and on 
the other that "some history is to be studied," or that 
" some metaphysics are to be studied," and the victory 
will easily be gained by those who hold the affirmative. 
When arguing with an opponent, let it be your business 
to prove the contradictory of his position ) and you niay 
insist on his proving not the mere sub-contrary of your 
statement, but the contrary or contradictory. In all 
cases it is desirable that we should know what is the con- 
tradictory (s'/ley%oc) of the proposition we are holding 
or impugning. 

4:1. The following are the transposed propositions we may oh 
tain by means of Opposition : 

If A be true, E is false, I true, false. 

If A be false, E is unknown, I unknown, O true. 

If E be true, A is false, I false, true. 

If E be false, A is unknown, I true, unknown. 

If I be true, A is unknown, E false, unknown. 

If I he false, A is false, E true, true. 

If be true, A is false, E unknown, I unknown. 

If be false, A is true, E false, I true. 

From the truth of a universal or falsehood of a particular, we maj 
titer the quality of all the opposed propositions ; but from the false 
8 



114 JUDGMENT 

hood of a universal or truth of a particular we can know only tlw 
quality of the contradictory. 

42. It should be observed that both in Conversion and 
Opposition we gain the Implied Judgments simply by the 
contemplation of the Extension together with the involved 
Comprehension of the Notions. In Subalternation, if A 
be true, I must be true, because I is involved in the Ex- 
tension of A. If A be true, E is false, for in A we ascribe 
an attribute to all A and in E we deny it. In all the 
transposed judgments we must see that the judgment 
reached has not a greater Extension than the judgment 
given, and that we predicate of both the same attribute 
or group of attributes. 

43. Conversion and Opposition are treated of in all the oldei 
logical treatises, in which, however, it is not noticed that the prop- 
ositions reached, are drawn by a contemplation of the Extension 
and Comprehension of the Notions. Nor has it been explicitly 
stated that the above rules of Conversion and Opposition do not 
apply to propositions in which there is no concept. Of such all Con- 
version is Simple, and all Opposition is Contradictory ; thus it 
being stated that " Newton discovered the law of gravitation," it 
would be unmeaning to say, by the law of subalternation, that 
" some Newton discovered the law of gravitation." Later logi 
cians have noticed that there are other Immediate Inferences equally 
entitled to a place in the exposition of Logical Judgment. It may 
be doubted whether they have seen their exact nature. 

44. Tlie Interpretation of Judgments gives certain Im- 
plied Propositions. If it be given "the orbit of the 
planets is elliptical," we have by Denomination " the epi- 
thet elliptical may be applied to the orbits of the planets ; " 
by Extension, " the orbits of the planets are among the 
things that are elliptical," and by Comprehension " ellip- 
tical is an attribute of the planetary orbits." Like Trans- 
posed Judgments may be derived from propositions in E, 
I, and O : as I, " some metals are lighter than water," 
by Denomination the phrase " lighter than water " may 
be applied to " some metals ; " by Extension " some 



IMPLIED JUDGMENTS. 115 

metals may be included in the things which are lighter 
than water ; " by Comprehension " the property of lighter 
than water belongs to some metals." Propositions in U 
may always be interpreted by Denomination and Com- 
prehension. It being given that " Ethics is the science 
of man's motive and moral nature," we may say " the 
phrase science of man's motive and moral nature may be 
applied to Ethics," and " the attributes of the science of 
man's motive and moral nature belong to Ethics." 

4o* There are Implied Judgments obtained by the 
special consideration of the Comprehension of the No- 
tions, as by 

TJie Interpretation of Marks, as when it is said "John 
loved Jesus," it is implied that " John lived " and that 
" Jesus lived," and that " there is such a thing as love." 

4z6» Added Marks to both subject and predicate. Thus 
if it be declared that " a negro is a fellow-creature," we may 
say " a negro in suffering is a fellow-creature in suffering." 
If " learning be useful " then " injury to learning would 
be injury to what is useful." 

47. Added Subject and Predicate may give other judg- 
ments by being added to a conception. Thus as " hon- 
esty is the best policy," " the disregard of honesty would 
be the disregard of the best policy." 

48. A Summation of Predicates may give us an Im- 
plied Judgment. Thus if it is found (1) that virtue is 
voluntary, (2) in obedience to a law, which is (3) the law 
of God, then we may combine the predicates and get a 
definition of virtue : " Virtue is a voluntary act done in 
obedience to the law of God." 

A9. Privative Conceptions may yield Transposed Judg- 
ments. We have seen (Part I., § 53) that from any given 
concept we obtain another by leaving out its mark : thus 
from the positive concept " wise," we may obtain the 
privative concept "unwise." Any judgment pionounceO 



116 JUDGMENT. 

on the positive concept, implies judgments upon the 
privative. 

The following is taken from Thomson's Outlines of the Laws of 
Thought (see also De Morgan's Formal Logic, p. 61), leaving out the 
examples in Y : 

I. A All the righteous are happy. 

None of the righteous are unhappy. 
All who are unhappy are unrighteous. 

E No human virtues are perfect. 
All human virtues are imperfect. 
No perfect virtues are human. 

I Some possible cases are probable. 

Some possible cases are not improbable. 
Some probable cases are not impossible. 

U The just are all the holy. 
All unholy men are unjust. 
No just men are unholy. 

[I. A All the insincere are dishonest. 
No insincere man is honest. 
All honest men are sincere. 

E No unjust act is unpunished. 
All unjust acts are punished. 
All acts not punished are just. 

I Some unfair acts are unknown. 
Some unfair acts are not known. 
Some unknown acts are not fair. 

O Some improbable cases are not impossible. 
Some improbable cases are possible. 
Some possible cases are not probable. 

U The unlawful is the only inexpedient. 
The lawful is the expedient. 
The lawful is not the inexpedient. 

We may make a proposition assume any one of these forms as 
may seem best fitted to give clearness of thought and to enable us 
to affirm or deny it ; and we may express it in the form which may 
best accomplish the end we have in view in the expression. It is 
by this process that from 0, " some mathematicians have not had 



IMPLIED JUDGMENTS. 117 

much practical wisdom," we get "some without practical wisdom 
have been mathematicians," (§33.) From any one of the abo\e 
propositions (except those in Oj we may derive another proposition 
by conversion. 

50. Conditional Propositions give implied judgments. 
" If this man has consumption he will not recover." This 
implies that the " case of a man who has a consumption 
is the case of a man who will not recover," or bringing 
the notions into closer relation, " One who has consump- 
tion will not recover." 

51. Disjunctive Propositions involve other propositions. 
Thus if it be allowed that " every given time must be 
spring, or summer, or autumn, or winter," we are entitled 
from the rule of Logical Division, that the members must 
make up the whole (I., § 58), to say, that " all times not 
spring, or summer, or autumn, must be winter," and from 
another rule, that the members must exclude one an- 
other (I., § 59), to affirm that " winter is neither spring, 
nor summer, nor autumn." 

52. In all these cases the rule is to be rigidly observed, 
that a term must be distributed in the transposed prop- 
osition only when it is distributed in the original one. 
Because we are entitled to make a predication of some, 
we are not therefore entitled to make the same predication 
of aU. 

53. The above are examples of Implied Judgments 
derived according to rules specified. We believe there 
may be other kinds drawn by discursive thought, and 
that the logician could formulize the law which rules 
them. It may be interesting to show how many other 
propositions could be got from the single one " men are 
responsible," by simply contemplating the Extension and 
Comprehension of the Notions. 

Extension. 
Every man is in the class responsible. 
This man is responsible. 



118 JUDGMENT. 

.Some men are responsible. 

Every tribe of mankind are responsible. 

Some responsible beings are men. 

It is not true tbat no men are responsible. 

It is not true that some men are not responsible, &c &c 

Comprehension. 

Man exists. 

Responsibility is a real attribute. 

Responsibility is an attribute of every man. 

Responsibility is an attribute of this man. 

Responsibility is an attribute of every tribe of mi-n. 

Responsibility is an attribute of some men. 

Irresponsibility may be denied of all men. 

No man is irresponsible. 

Irresponsible beings are not men. 

Men of wealth are responsible with their wealth. 

To punish men is to punish responsible men, &c, &c. 
In treating of Implied Judgments we have been indebted tc 
Thomson's Outlines of the Laics of Thought, where, however, they 
are called Immediate Inferences and placed under Reasoning, aud 
are not derived from the nature of the Notions. 

#4. We may close the part of Logic which treats of 
Judgment, by showing what Logic can do in settling for ns 
what are and what are not true propositions. It is evi- 
dent that it cannot determine for us directly what prop- 
ositions imply and what do not imply Objective reality, 
e. g., whether there is or is not a sea-serpent. But it can 
do much in the way of enabling us to pronounce a right 
judgment upon evidence. It requires us to ascertain what 
are the Notions, that is, the things compared and in regard 
to which we make the affirmation or denial. It makes us 
look at the nature of the notions and find whether they 
are singulars, abstracts, or general concepts, and to de- 
cide about them accordingly. Thus when it is said that 
" virtue is that which promotes the greatest happiness," 
we see that both subject and predicate are abstracts, and 
that therefore the terms must be convertible (§ 14) ; and 
as we see this, we are better able to determine whethei 



IMPLIED JUDGMENTS. 119 

the proposition is true, for we ask whether " that which 
promotes the greatest happiness is (always) virtue ? " If 
it be maintained that "sea-serpents exist," we perceive 
that serpent is a common term, and we inquire what are 
the common qualities (differentia) of serpents, and are 
thus in a better position to determine whether serpents 
can exist in the sea, and whether the appearances which 
sailors have noticed can be of sea-serpents. Logic urges 
us farther to inquire into the relation of subject and 
predicate, whether it is one of equivalence or attribution. 
Every one will admit the truth of the attributive prop- 
osition that " virtue promotes happiness," but many deny 
the truth of the equivalent one, "that which promotes 
happiness is virtue." We believe that more than one 
half of the error in the world proceeds not from mere 
ignorance, but from inattention and confusion, which find- 
ing us ignorant, tends to keep us in ignorance. Logic 
helps to cure the evil by requiring of us to determine 
what are the notions, and to place these fully and fairly 
before the mind ; and when this is done, we will be able 
either to see what judgment we should pronounce, or to 
wait for further light before we come to any decision. 



PART THIRD. 

REASONING 



1. " In every instance in which we reason, in the strict 
sense of the word, i. e., make use of arguments (I mean 
real, i. e., valid arguments), whether for the sake of refut- 
ing an adversary, or of conveying instruction, or of satis- 
fying our own minds on any point, whatever may be the 
subject we are engaged on, a certain process takes place 
in the mind which is one and the same in all cases, pro- 
vided it be rightly conducted. Of course it cannot be 
supposed that every one is even conscious of this process 
in his own mind ; much less is competent to explain the 
principles on which it proceeds. This indeed is, and can- 
not but be, the case with every other process respecting 
which any system has been formed ; the practice not only 
may exist independently of the theory, but must have 
preceded the theory. There must have been Language 
before a sj'stem of grammar could be devised ; and mu- 
sical compositions previous to the science of Music. This, 
by the way, will serve to expose the futility of the popular 
objection against Logic, that men may reason very well 
who know nothing of it. The parallel instances adduced, 
show that such an objection might be applied in many 
other cases where its absurdity would be obvious ; and 
that there is no ground for deciding thence, either that the 
system has no tendency to improve practice, or that even 



ITS NATURE. 121 

if it had not, it might not still be a dignified and interest- 
ing pursuit." 

2° It will be shown that the principles involved in the 
reasoning process are one and the same, whatever be the 
things about which we argue, be they material, or mental, 
or moral, or mathematical, or political, or theological. 
" One of the chief impediments to the attainment of a 
just view of the nature and object of Logic, is the not 
fully understanding, or not sufficiently keeping in mind, 
the sameness of the reasoning process in all cases. This 
error may at once be illustrated and removed by consider- 
ing the parallel instance of Arithmetic, in which every 
one is aware that the process of a calculation is not af- 
fected by the nature of the objects whose numbers are 
before us ; but that (e. g.) the multiplication of a number 
is the very same operation, whether it be a number of 
men, of miles, or of pounds." Nor is Logic to be regarded 
as a peculiar method of reasoning, " which is in fact as 
great a blunder as if any one were to mistake grammar 
for a peculiar language, and to suppose it possible to 
speak correctly without speaking grammatically." 

3. " Supposing it then to have been perceived that the 
operation of reasoning is in all cases the same, the analy- 
sis of that operation could not fail to strike the mind as 
an interesting matter of inquiry. And moreover, since 
(apparent) arguments which are unsound and inconclusive, 
are so often employed, either from error or design, and 
since even those who are not misled by these fallacies are 
so often at a loss to detect and expose them in a manner 
satisfactory to others, or even to themselves, it could not 
but appear desirable to lay down some general rules of 
reasoning applicable to all cases, by which a person 
might be enabled the more readily and clearly to state 
the grounds of his own conviction, or of his objection 
to the arguments of an opponent, instead of arguing at 



122 REASONING. 

random without any fixed and acknowledged principles 
to guide his procedure. Such rules would be analogous 
to those of Arithmetic, which obviate the tediousness and 
uncertainty of calculations in the head ; wherein after 
much labor, different persons might arrive at different 
results, without any of them being able distinctly to point 
out the error of the rest. A system of such rules, it is 
obvious, must, instead of deserving to be called ' the arc 
of wrangling,' be more justly characterized as ' the art 
of cutting short wrangling' by bringing the parties to 
issue at once, if not to agreement, and thus saving a 
waste of ingenuity." — "Whately's Elements, Analytical Out- 
line. 

4« In Judgment Proper, we compare immediately the 
two notions, that is, the things apprehended, and declare 
their agreement. But there are cases in which we do not 
perceive the relation of the notions immediately, but in 
which we may discover them mediately, by means of a 
third or mediating notion. Thus I wish to know whether 
John the Baptist was a priest, and I cannot pronounce au 
immediate judgment, for it is not expressly said in Scrip- 
ture that he was a priest. But we remember that his 
father Zacharias was a priest, and using son of a priest aa> 
a middle term, and finding from the Old Testament that the 
sons of priests were themselves priests, we argue that " the 
Baptist, being the son of a priest, was a priest." Here, it 
will be observed, we have three terms, the two terms we 
wish to compare, " Baptist " and " priest," and the term 
by which we compare them, " son of a priest." In the 
discursive process, when we analyze it, there will be found 
three acts of comparison : one in which we compare one 
of the original terms with the middle ; a second in which 
we compare the other original term with the middle ; and 
the third in which we bring the two terms, which we 
have compared separately with the middle, into compar- 



ITS NATURE. 123 

ison with each other. This is Seasoning which is denned 
as " the act of proceeding from certain judgments to 
others founded on them." 

5. To bring out the acts of comparison involved, we 
an fold them in three propositions : 

The sons of priests were priests ; 
The Baptist was the son of a priest ; 
The Baptist was a priest. 

When reasoning is thus analyzed and expressed, it is 
called a Syllogism. 

6. The syllogistic analysis of reasoning, so far as is known, was 
first unfolded by Aristotle in the Prior Analytics, and. constitutes 
the most certain, and altogether the greatest, discovery ever made 
in mental science. It has been discussed, and attempted improve- 
ments made on it, by commentators on Aristotle, by the medieval 
scholastics, by the logicians of the 17th century, and by modern 
writers from Kant to the present time. 

7. Some have thought that we can reason from on« 
judgment. And it is quite true that from any one judg- 
ment we -can draw others immediately in the mode ex- 
plained in speaking of Implied Judgments. But the 
judgments thus reached are confined within very narrow 
limits. When we have two judgments in a certain rela- 
tion to each other, a much wider range of judgments can be 
drawn, and the process involved constitutes Mediate 
Reasoning, or Reasoning Proper. It often happens, in- 
deed, that in reasoning thus understood, there is only 
one judgment expressed in what is given or allowed. But 
if we carefully examine the process it will be found that 
there is another judgment, which though suppressed in 
statement, is involved in thought. A man has taken ar- 
senic and we conclude that he shall die. Here are two 
judgments implied in order to the validity of the reasoning. 
One is, the matter of fact that he has taken arsenic ; and the 
other, the general fact that he who has drunk arsenic shall 
die. We may not think it necessary to enunciate both of 



124 REASONING. 

these. We would not mention the one to a person who 
had seen him take the arsenic ; we would not announce 
the other to a man who knew that arsenic was poison. 
But we would have to state both to one ignorant of both ; 
and both if not explicitly announced are implicitly im- 
plied in the reasoning. 

An argument with one premiss suppressed is vulgarly called an 
Entliymeme. Aristotle, however, defines Entbymeme tvdv/i?//u.a /uiv 
ovv iarl avXAoyicjuog e? elkotov f/ arj/aeiuv (Anal. Pr. II., 27. See Ham- 
ilton's Discussions, Art. Logic, and Trendelenburg Elementa, § 37). 

8, In a syllogism as an analysis of the reasoning pro- 
cess we must have, as we have in the reasoning process 
itself, three, and no more than three terms : the two 
whose agreement or disagreement we are seeking to deter- 
mine, and a third by which we determine it. The two first 
are called the Extremes, and the third the Middle. Again 
in a syllogism, in order to unfold the relation of the three 
terms, there must be three propositions, two in which we 
compare each of the Extremes with the Middle, and a 
third in which we compare them with each other. The 
two first are the Premisses, and the third the Conclusion. 
It is evident that the Middle term will appear in each of 
the premisses, but not in the conclusion. The laws of 
discursive thought do not require us to follow any order 
in the arrangement of the three propositions. What we 
have to look at is the relation of the terms ; and if we 
bring out this, it is no matter whether we begin with the 
premisses, or which of the premisses we place first. Thus 
instead of the order followed above, we might say, 

The Baptist was a priest ; 
for, He was the son of a priest ; 
and, The sons of priests were priests. 

From these definitions and general statements we may 
derive certain Rules, which are applicable to reasoning of 
every kind. 



ITS RULES. 125 

0. (1) In a syllogism there should only be three terms. 
This has already been explained. 

10. (2) In a syllogism there can only be one middle 
term. It is only thus we can bring the extremes into 
comparison. When a middle term is ambiguous we may 
have two middle terms in sense though not in sound ; 
and we are ever liable to compare the one extreme with 
the middle used in one sense, and the other extreme with 
the middle in another sense. Hence the fallacy of Am- 
biguous Middle which will often fall under our notice. 

11. (3) One premiss must be affirmative. In other 
words two negative premisses prove nothing. For unless 
there be an affirmative judgment declaring the agree- 
ment of the middle with one of the extremes, there can be 
no inference about the terms which we wish to compare. 
Two negative judgments simply declare that there is no 
relation between the middle term and the extremes, and 
authorize no judgment as to the relation of the extremes. 

12. (4) If either premiss is negative, the conclu- 
sion must be negative. For one of the premisses being 
negative, the other is affirmative, and so in one premiss 
we assert that the middle disagrees with one extreme, 
and in the other that it agrees with the other extreme, 
and if so the extremes must disagree with one another. 

13. (5) To prove a negative conclusion one of the 
premisses must be negative. We cannot argue that 
there is no connection between the extremes till we have 
shown that there is no connection between one of the ex- 
tremes and the middle. 

14. The question now rises, can we determine and 
3nunciate what is the principle in the mind which 
regulates reasoning. The answer is that this can be 
done by carefully observing examples of valid reasoning, by 
ascertaining what is common to them all, and expressing 
this in a general formula. The rule in its most general 



126 REASONING. 

form is, that "notions which agree with one and the 
same notions agree with one another." This for affirm- 
atives, and for negative conclusions, "notions, one of 
which agrees, while the other disagrees with one and the 
same notion, disagree with each other." But in such a 
rule the phrases ''agree" and "disagree" are wide and 
vague, and it is desirable to become more particular ana 
specify the nature of the agreement. The distinction 
which we have drawn between percepts and abstracts 
on the one hand and concepts on the other (P. I., § 38) 
leading to the distinction between propositions in which 
the relation is one of equivalence, and those in which it is 
one of joint extension and comprehension (P. II., § 14, 
i.5), will help us here, and show us two regulating princi- 
ples emerging for two kinds of reasoning. 

15. FIRST REGULATING PRINCIPLE. "No- 
tions equivalent to one and the same third notion are 
equivalent to one another ; " and for negative reason- 
ing " notions, one of which is equivalent and the other not 
equivalent to one and the same notion, are not equivalent 
to one another." This dictum rules all reasonings in 
which the three notions are Percepts or Abstracts. 

Shakespeare wrote Hamlet ; 

He wlio wrote Hanilet is tlie greatest English poet ; 
.-. Shakespeare was the greatest English poet. 

Under this same head I place the following, and in- . 
deed most arithmetical and geometrical inferences : 

A = B 

B = C 

•. A = C 

In all ratiocination of this description, the subject of 
each of the propositions may be made the predicate, and 
the predicate the subject, and the reasoning will be valid 
and formally correct. 



REGULATING PRINCIPLES 127 

He who wrote Hamlet was Shakespeare , 
He is the greatest English poet who wrote Hamlet , 
.'. The greatest English poet was Shakespeare. 

In these and in like propositions, the terms are per- 
cepts or abstracts, and the relations in the propositions 
and in the argument is of identity or of equality. It is 
of great moment to separate these simple cases of reason- 
ing from more complex ones, to be immediately consid- 
ered, in which we have concepts, and extension, and 
minor and major terms, and mood and figure. 

16. We are now in a position to understand what we should 
make of the unfigured syllogism of Hamilton. 

Copperas and sulphate of iron are identical ; 
Sulphate of iron and sulphate of copper are not identical ; 
/. Copperas and sulphate of copper are not identical. 
Here he has turned " identical," which is neither less nor more 
than the copula, into a separate term. The reasoning should stand 
t,hus : 

Copperas is sulphate of iron ; 
Sulphate of iron is not sulphate of copper ; 
.•. Copperas is not sulphate of copper. 

17. SECOND REGULATING PRINCIPLE. "What- 
ever is predicated of a class may be predicated of all the 
members of that class." In the affirmative form, the Dic- 
tum de omni, it is, " Whatever is affirmed of a class may 
be affirmed of all the members of the class." In the nega- 
tive form, the Dictum de nullo, it is, " Whatever is denied 
of a class may be denied of all the members of the class." 
It is otherwise expressed, " Whatever is predicated of a 
concept distributed may be predicated of all that is con- 
tained in the concept." This is the famous Dictum of 
Aristotle, which has been held to be the regulating prin- 
ciple of reasoning by most logicians from the time of the 
Stagyrite. We hold it to be the true regulating principle 
in all reasoning in which there is a General Notion. It 
must be so from the very nature, from the very meaning, 
of a General Notion, and the employment of it in reason- 



128 REASONING. 

ing. For it will be found that in the reasoning which 
contains a concept, there is a predication in regard to the 
concept generally, and a predication in regard to a class 
or individuals contained in it, and the conclusion is 
necessitated by the two, or rather by the relation 
of the two, the one embracing the other in its exten- 
sion. 

18. At this point it will be necessary to explain some 
terms which are found in attributive (but not in equiva- 
lent) reasoning. The subject of the conclusion is called 
the Minor Term, and the predicate the Major Term : 
this because the Minor Term (at least in affirmative 
propositions, P. II., § 17) is the least extensive, and the 
Major Term the more extensive. The premiss containing 
the Major Term is called the Major Premiss — sometimes 
also the Sumption ; that containing the Minor Term, the 
Minor Premiss — or the Subsumption ; and this, which- 
ever of the premisses is placed first. 

From the time of Aristotle to that of Boethius, the minor premiss 
was placed first — following the analytic mode ; from the time of 
Boethius it has been customary to put the major premiss first — fol- 
lowing the synthetic method. 

19. The Dictum of Aristotle is the regulating princi- 
ple of all reasoning in which there is a Concept. But in 
order to secure that arguments be put in correct form, 
logicians lay down certain rules derived from it. Those 
rules are additional to those given above (§ 9-13), as 
applicable to all reasoning. 

20. (1) The middle term must be distributed at least 
once (by being the subject of a universal or predicate of 
a negative). For if it were taken only in part, it might 
happen that in the one premiss we compared an extreme 
with one part of the middle, and in the other premiss the 
other extreme with another part of the middle, and thus 
entirely failed to bring the extremes into comparison 



RULES. 129 

When this rule is violated, we have the fallacy of Undis- 
tributed Middle : 

All good men are sincere ; 
Eousseau was sincere ; 
.•. Rousseau was a good man. 

Here the Middle Term is undistributed in both premi- 
ses, being the predicate of two affirmatives (P. II., § 11). 
What we have done is to declare that all good men are 
among the " sincere," that Rousseau is among the " sin- 
cere ;" but then Eousseau may be among the sincere, and 
not among the good, of whom it is said that they are 
among the sincere, but not that they are coextensive 
with the sincere. But it is enough that the middle be 
once distributed, for as one extreme has been compared to 
the whole of the middle, even though the other be com- 
pared to only a part, we have brought the two into com 
parison. 

21. (2) No term must be distributed in the conclu . 
sion which has not been distributed in one of the premis- 
ses. Otherwise we should be using a term in its entire 
extent in the conclusion when we had only made a com- 
parison of it in part of its extent in the premiss. The 
violation of this rule is called an Illicit Process of the 
Major or Minor Term, according as it is the major or 
minor term which is thus illegitimately used. 

Whatever gives pleasure is to be valued ; 
The learning of logical formula? does not give pleasure ; 

is not to be valued. 
Here " to be valued " is taken only in part in the pre- 
miss, being the predicate of an affirmative, whereas it is 
taken in all its extent in the conclusion, and we have an 
illicit process of the major term. 

22. (3) From two particular premisses, no conclusion 
can be drawn. For if they were both negative (0 O), yon 
could get no inference (§ 11). If they were both affirm- 

9 



130 REASONING. 

ative (II.), the middle would be undistributed in either 
premiss (P. II, § 11). There is left only I O, where trie 
negative conclusion makes the major term distributed, 
which it is not in the major premiss ; and 01 with either 
undistributed middle or illicit process of major. 

23. (4) If one of the premisses be particular, the con- 
clusion must be particular. By a like process to that fol- 
lowed in Kule (3), it can be shown that the violation of 
this rule implies an illicit process of the minor. 

2d. It should be observed that these rules apply simply to reason- 
ing in which we have a concept. The rules given from § 9 to § 13, 
apply to all reasoning. The main rules are summed up by logi- 
cians in the following mnemonic lines: 

Distribuas medium ; nee quartus terminus adsit. 
Ultraque nee prsemissa negans, nee particularis. 
Sectetur partem conclusio deteriorem. 
Et non distribuat, nisi cum prsemissa, negetve 
To understand the third line, that the conclusion follows the 
worse part, it is necessary to bear in mind that logicians reckon the 
particular as worse than the universal, and the negative worse than 
the affirmative. 

23. MOODS. By Mood is meant the legitimate forms 
of the syllogism indicated by the symbolic vowels A, E, I, 
O, designating the quantity and quality of the proposi- 
tions in then" respective order. 

E No planet twinkles ; 
A That body twinkles ; 
.•. E It is not a planet. 

As there are four kinds of propositions, and three 
propositions in each syllogism ; and as any one of the 
four may be the major premiss ; and each of the four 
majors may have four different minors ; and each of the 
sixteen pairs of premisses may have four different con- 
clusions, it might look as if the possible moods might be 
4 x 4 (= 16) x 4 = 64. But many of these moods are 
illegitimate as violating the rules of the syllogism as 
above laid down (§ 20-23) ; some from negative premisses. 



FIGURES. 131 

some from particular premisses, &c. When sifted it will be 
found that there remain only eleven legitimate moods, 
AAA, AAI, AEE, AEO, All, AOO, EAE, EAO, EIO, IAI, 
OAO. 

26. The rest are excluded for the following reasons : 
EBA, EBB, EBI, EEO, EOA, EOE, EOI, EOO, OEA, OEE, OEI, 

OEO, OOA, OOE, OOI, 000, = 16 for negative .premisses. 

II A, HE, III, 110, IOA, IOE, 101, 100, 01 A, OIE, Oil, 010, 
= 12 for particular premisses. 

ABA, AEI, AOA, AOI, EAA, EAI, EIA, EII, IEA, IEI, OAA, 0A1, 
= 12, because of a negative premiss without negative conclusion. 

AIA, AIE, AOE, EIE, IAA, IAE, IEE, OAE, =.8, because of a 
particular premiss without particular conclusion. 

AAE, AAO, AIO, IAO, = 4, because of negative conclusion with 
out negative premiss. 

IEO is rejected for an illicit process of the major in every figure. 

27. FIGURE. This consists in the position of the 
middle term in reference to the extremes. As the middle 
term is the very bond of the argument, syllogisms may be 
divided very conveniently in respect of figure. In the 
First Figure, the middle term is the subject of the major 
premiss and predicate of the minor. In the Second Fig- 
ure it is the predicate of both premisses. In the Third 
Figure it is the subject of both. In the Fourth Figure it 
is the predicate of the major premiss, and subject of the 
minor. Let P stand for the major term (the predicate of 
the conclusion) ; S for the minor term (the subject of the 
conclusion) ; and M for the middle term. 

28. Fig. I. M P A All human beings are responsible to God ; 

S M A The negro race are human beings ; 

S P A They are responsible to God. 
The Dictum is applicable at once to an argument in 
this figure. We affirm P (responsible) of M (human 
beings), and M (human beings) of S (negroes), and in 
the conclusion we affirm P (responsible) of S (negroes). 
This figure admits of four moods, AAA, EAE, All, EIO. 
From this it appears that it admits of conclusions in everv 



132 REASONING. 

kind of proposition, A, E, I, O ; and it is the only figure 
in which a universal affirmative (A) can be drawn. We 
shall see when we come to consider Reduction that every 
kind of argument can be made to take this form ; but 
there are arguments which fall naturally into other 
figures. 

29. There are Special Rules to guide us in detennining what are 
legitimate moods in each figure. Thus for the first figure : (1) The 
minor premiss must be affirmative ; for if it were negative the con- 
clusion must be negative and distribute the major term (P), which 
would not be distributed in the major premiss, whicb must be af- 
firmative when the minor is negative. (2) The major premiss must 
be universal ; for if it were particular, the middle term (M) would 
not be distributed in the major premiss, and could not be distributed 
in the minor premiss as being the predicate of an affirmative. 

30. Fig. II. P M A Reptiles bring forth their young by eggs ; 

S M E The rat does not bring forth its young by 

eggs ; 
S P E The rat is not a reptile. 
Arguments fall naturally into this figure when we 
have to disprove something which has been maintained 
or believed (as when we prove that the rat is not a rep- 
tile), or when we have to bring out the differences of 
things, which we do by the negative premisses and con- 
clusion. 

31. The Special Rules are (1) One of the premisses must be 
negative, to admit of M being distributed. (2) The conclusion 
must be negative, because of the negative premiss. (8) The major 
premiss must be universal, for the conclusion being negative dis- 
tributes P, which must be distributed in the premiss. The special 
regulating principle is the Dictum de Diver so, " if one term is con- 
tained in, and another excluded from, a third term, they are mu 
family excluded." 

32. Fig. III. M P A The connection of soul and body is to be 

believed ; 
MSA The connection of soul and body is incom 

prehensible ; 
S P I Some things incomprehensible are to be 

believed. 



FIGURES. 133 

Arguments fall into this form when the middle term is 
singular, since a singular term is naturally the subject 
when the predicate is a concept. It is, therefore, useful 
in bringing in examples. It is also efficient in establish- 
ing an exception to an opponent's premiss, when his argu- 
ment requires the premiss to be universal. Thus, some 
one maintains that certain Scripture doctrines are not to be 
believed, as they are incomprehensible. In order to the 
validity of his argument it is rsecessary to assume as his 
major premiss, that " everything incomprehensible is not 
to be believed " (E). Now we can, as in the example, 
show iu opposition to him, that " some things incompre- 
hensible are to be believed " (I), which is the contradic- 
tory of his major premiss. 

33. The Special Rules : (1) The minor premiss must be affirma- 
tive. For if it were negative the conclusion would be negative, and 
would distribute P, which cannot be distributed in the major pre- 
miss, which must be affirmative when the minor is negative. (2) 
The conclusion must be particular, otherwise there would be an 
illicit process of the minor, which as the predicate of an affirmative 
is not distributed in the premiss, and cannot therefore be distrib- 
uted in the conclusion. Its special rule is the Dictum de exemplo, 
" Two terms which contain a common part partially agree, or if one 
contains a part which the other does not, they partially differ." 

34. Fig. IV. P M A What is expedient is conformable to nature ; 

M S E What is conformable to nature is not hurt- 
ful to society ; 
S P E What is hurtful to society is not expedient 
The Special Rules are (1), Major premiss not 0, else illicit maj "i 
(2) Minor premiss not 0, else middle not distributed. (3) Conclu 
sion not A, else illicit minor. 

35. The fourth figure is not found in Aristotle, and many logi- 
cians have rejected it. In the minor premiss, S, the predicate is 
more extensive than M, the subject ; and in the major premiss, M. 
the predicate is more extensive than P; consequently S is more 
extensive than P. But in the conclusion we find S, the more exten- 
sive, the subject, and P, the less extensive, the predicate, which is 
not agreeable to spontaneous thought, and should not have a place 
in reflective thought. Figure fourth is perfectly valid, but is not a 



134 REASONING. 

form into which thought spontaneously falls. It is reached by con- 
version or other forms of transposed judgments. To take the ex- 
ample (Whately's) : the conclusion is not in the form which natu- 
ral thought would use ; we should rather say, " What is expedient 
is not hurtful to society." This makes "what is expedient " which 
has been placed as if narrower than " conformable to nature "in the 
first premiss, which has again been placed as if narrower than " hurt- 
ful to society " in the second premiss, to take its proper place in the 
conclusion as the subject, as narrower than " hurtful to society " in 
the predicate. But in this collocation the reasoning is in the first 
figure, which is its natural form. 

What is conformable to nature is not hurtful to society ; 
What is expedient is conformable to nature ; 
What is expedient is not hurtful to society. 

30. Mnemonic Lines, devised to exhibit the available 
moods in each figure, and also to assist in Reduction. 

Fig. I. bArbArA, cElArEnt, dArll, fErlOque prioris ; 

Fig. II. cEsArE, cAmEstrEs, fEstlnO, bArOKO, secundte ; 

Fig. III. tertia, dArAptl, dlsAmls, dAtlsI, fElAptOn, 

bOkArdO, fErlsOn, habet ; quarta insuper addit. 

Fig. IV. brAmAntlp, cAmEnEs, dlniArls, fEsApO, frEsIsOn. 
Quinque subalterni totidem generalibus orti, 
Nomen habent nullum, nee si bene colligis, usum 

In these lines the vowels indicate the mood of the syl- 
logism, e. g., AEE in Camestres (Fig. II.) denotes that 
the major premiss is universal affirmative, and the minor 
premiss and conclusion both universal negative. The 
five subaltern moods which might be drawn, are AAI, 
EAO, in Fig. I. ; EAO, AEO, in Eig. II., and AEO, in 
Fig. IV. ; but they are useless, as universals can be 
drawn, and they are comprised in AAA, EAE, EAE, 
AEE, AEE. 

37. REDUCTION. In this we bring a syllogism in 
one Figure into the form of a syllogism in another. It is 
possible to reduce syllogisms in the first figure to syllo- 
gisms in the others. But the phrase is specially applied 
to that process in which we turn syllogisms of the second, 
third, and fourth figures into the first. The object of re 



REDUCTION. 135 

duction is first to show that the Dictum of Aristotle, 
which is obviously the regulating principle in the firsi 
figure, is truly the regulating principle in all reasoning — 
in which a concept is involved. But it shows secondly, 
and in a very interesting way, that the reasoning process, 
whatever be the forms which it takes spontaneously, or 
those in which it is made to appear by logicians in order 
to bring out the nature and validity of the process, is in 
all cases one and the same in substance and in principle. 

38* The reduction is made in every instance by Im- 
plied Judgments, specially by Conversion ; that is, we put 
one or more of the propositions in a transposed form. 
The mnemonic lines are meant to direct us in this. The 
initial consonants b, c, d, f, show that the mood so marked 
in the second, third, and fourth figures, is to be reduced 
to the mood marked by the same letter in the first. Thus 
c in camestres, shows that tbe syllogism is to be reduced 
to celarent in the first. The consonants in the middle 
of the words, show how the reduction is to be effected. 
Thus s indicates that the proposition designated by the 
vowel before it, is to be converted simply ; p, that it is to 
be converted per accidens ; and m, that the premisses be- 
tween which it stands are to be transposed. The k in 
baroko and bokardo denotes that the mood is to be re- 
duced per impossibile — a process to be explained forth- 
with. 

39. Ostensive Reduction is accomplished directly bj 
Conversion and other Implied Judgments. We may give 
an example from each figure : 

Fig. II. cA All men have the power of speech ; 

mEs Gorillas have not the power of speech; 
trEs Gorillas are not men. 

reduced to cE Beings having the power of speech are nol 
gorillas : 
1A All men have the power of speech ; 
rEnt Gorillas are not men. 



136 



REASONING. 



Fig. III. dA Theft is a crime ; 

tls Some kinds of theft were encouraged by the 
laws of Sparta ; 
I Some of the things encouraged by the laws of 
Sparta were crime ; 
reduced to dA Theft is a crime ; 

rl Some things encou raged by the laws of Sparta 

were theft ; 
I Some things encoura ged by the laws of Sparta 
were crime. 
Pig. IV. brA Political economy is a profitable study ; 
mAn Profitable study sharpens the intellect ; 
tip Among the things that sharpen the intellect is 
political economy, 
reduced to bAr Profitable study sharpens the intellect ; 
bA Political economy is a profitable study ; 
rA Political economy sharpens the intellect. 
4i0. Reductio per Impossibile. In this process we pro- 
ceed on the principle that of two contradictory proposi- 
tions, one must be true and the other false. We prove 
not that the original conclusion is true, but that its con- 
tradictory must be false. By it the older logicians re- 
duced the syllogisms AOO in the second figure, and OAO 
in the third. The method of effecting it is indicated by 
baroho and bokardo in the mnemonic lines, where the 
letter k intimates that the proposition denoted by the 
vowel immediately before it must be left out, and the con- 
tradictory of the conclusion substituted : 
bO Some poets are not wise ; 
kAr Poets are men of genius ; 
dO Some men of genius are not wise. 
If this conclusion is not true, its contradictory must, 
' all men of genius are wise." Let this be substituted for 
the major premiss : 

bAr All men of genius are wise ; 
bA All poets are men of genius ; 
rA All poets are wise. 
This is the contradictory of the originally granted maioT 



REDUCTION. 137 

premiss, and must therefore be false. But one of the pre 
misses which proves a falsehood must be false. This 
cannot be the minor, which was one of the originally 
granted premisses ; it must therefore be the major. 
But this major thus shown to be false, is the contradictory 
of the original conclusion, which must therefore be true. 
The same mode of demonstration is employed for baroko, 
and may be employed in the reduction of all the moods 
of the second, third, and fourth figures. But it is not 
necessary to resort to this method. For while baroko 
and bokardo cannot be reduced by Conversion either 
simple or per accidens, they may by the Implied Judg- 
ments involved in Privative Conceptions, (Part II., 49J. 

dA All true poets are men of genius ; 
rl Some not wise are poets ; 
I Some not wise are men of genius ; 
or, Some men of genius are not wise. 

If we adopt this method, which is perfectly legitimate, 
quite as much so as that by conversion or contradictory 
opposition, then we require to substitute fakoro and 
dokamo in the place of baroko and bokardo in the mne- 
monic hues. 

4:1. Generally it may be remarked, that in all Mediate 
Reasoning we may use what are called Immediate Infer- 
ences. We may put either of the premisses or the con- 
clusion in the form of any Implied Judgment, if thereby 
we are enabled to see the relation of subject and predi- 
cate more clearly. Thus in the last example the conclu- 
sion may be expressed either " some men not-wise are 
men of genius," or " some men of genius are not wise." 
This enlarges indefinitely the number of forms in which 
reasoning may be expressed and still be valid. It is not 
necessary to spread out all the forms which reasoning 
may thus be made to take. It is enough to know what 



138 REASONING. 

we are entitled to do, and how to do it legitimately, wlien 
perspicuity of thought requires it. 

42. REASONING IN COMPREHENSION. In rea- 
soning, so far as we have considered it, the propositions 
have been understood in extension, and Aristotle's Dic- 
tum, which is a maxim in extension, has been considered 
the regulating principle. But we have seen tnat all prop- 
ositions have a meaning in comprehension. May there 
not then be reasoning in comprehension also? In an- 
swering this question fairly, it should be allowed that in 
the greater number of propositions, the uppermost thought 
is in comprehension rather than extension. When we are 
saying " the boy plays," we are thinking of the boy as 
engaged in the act of playing, rather than among the 
class of things that play. But it is different when we con- 
sider judgments so connected as to entitle us to draw a 
conclusion. The uppermost spontaneous thought seems 
now to be in extension. When we argue that " the Bed 
Indian, having the power of speech, is a human being," 
we refer, in thought, the Bed Indian to a class composed 
of those who have the power of speech. Of course the 
possession of attributes is implied in each of the terms ; 
but in the ratiocination we require to proceed on the 
principle that there are classes possessing the attributes ; 
and it is because this is recognized, that the conclusion is 
seen to follow, If we argue that "man, being respon- 
sible, is a free agent," the reasoning is conclusive only on 
the condition that the whole class " man " is in the class 
" responsible," which again is in the class " free agent." 
That " brutes have no free will " cannot give the conclu- 
sion that "the brutes are not responsible," unless we 
proceed on the general principle that "those who are 
without free will are not responsible." 

43. But then all the propositions in a syllogism may 
be understood in comprehension ; and a syllogism mav 



IN COMPREHENSION. 139 

be constructed in which the comprehension is the more 
prominent, and the reasoning will be perfectly valid, and 
the form accurate, though not the form expressing the 
thought which the mind spontaneously follows. The 
regulating principle will now be, " a part of a part of an 
attribute will be part of the whole attribute." 

Free will is an attribute of responsibility ; 

Responsibility is an attribute of man ; 
.'. Free will is an attribute ofmau. 

Bringing forth its young by eggs is an attribute of reptiles, 
Bringing forth its young by eggs is not an attribute of rats ; 
. ' . Some attributes not of rats are attributes of reptiles. 

It will be observed that the order of the terms in the 
propositions, is here the reverse of what it is when we 
express the thought in extension. In extension we say 
in the major premiss "man is responsible," "reptiles 
bring forth their young by eggs." In the form of exten- 
sion, the subjects are the less extensive and the more 
comprehensive ; and the predicates the more extensive, 
and the less comprehensive. But in comprehension the 
subjects are the more comprehensive and the less exten- 
sive, and the predicates the less comprehensive and the 
more extensive. 

What do we mean when we say that in reasoning in comprehen- 
sion the ruling principle is that " part of the part of an attribute 
is a part of the whole attribute ? " We mean, on the principle that 
the abstract implies the concrete, that whatever things contain a 
part must also contain a part of that part, e. g., that men, having 
the attribute of responsibility, have the attribute of free will in- 
volved in that responsibility. We seem thus to be thrown back on 
extension as the uppermost thought in reasoning. 

4:4:. But if it be true that the mind reasons primarily 
in extension, it is not necessary to draw out the forms in 
comprehension, the more so as the forms in extension 
embrace all cases of reasoning — except those proceeding 
on the principle of Equivalence, which we have placed 



140 REASONING. 

under a separate head (§ 15). But the student should ha 
able, on demand, to translate reasoning in extension, in 
the way above indicated, into reasoning in comprehen- 
sion. 

45. THE TWO DICTA ARE COMBINED. We 
have seen in our survey, that there is one rule so general, 
that it may be held as regulating all reasoning that " no- 
tions which agree with one and the same notion agree 
with one another " (§ 14). But this rule is too vague, as 
not specifying the nature of the agreement ; and so we 
lay down two more specific rules, the one the rule of 
Equivalence (§15), and the other the Dictum of Aris- 
totle (§ 17) — to which we may add the rule of Comprehen- 
sion — if we allow reasoning in comprehension (§42). 
But there are cases in which the rule of Equivalence and 
the Dictum are united : 

A Locke lived in the seventeenth century ; 
IT Locke is the greatest of English metaphysicians ; 
A The greatest English metaphysician lived in the seventeenth 
century. 

This is in the Third Figure, and yet we legitimately 
draw a universal conclusion, and the reason is that the 
minor term being an abstract is distributed, is distributed 
in the minor premiss, and may therefore be distributed 
in the conclusion. 

Both Dicta are involved in Mathematical reasoning, as 
in the demonstration of Euclid, B. I., Prop. I. 

(1) The radii of the same circle are equal to one another ; 
A C and A B are radii of the same circle (B C D) ; 

A C and A B are equal to one another. 

(2) The radii of the same circle are equal to one another ; 
B C and A B are radii of the same circle (ACE); 

B C and A B are equal to one another. 

(3) AC = AB;BC = AB/.AC = BC. 

Under this head should be placed what is called a Per- 
fect Induction, in which we argue that what we have 



THE TWO DICTA COMBINED. 141 

found true of each of the members of a class, must be true 
of the whole class. 

A Shein, Ham, and Japhet were in the ark ; 

U Sheui, Ham, and Japliet were the whole sons of Noah . 

A All the sons of Noah were in the ark. 

In both these examples, two of the terms are singulars 
involving a process of abstraction (but not of generali- 
zation) ; the minor premisses are equipollent, with both 
terms distributed ; and so the minor term is to be re- 
garded as distributed in the conclusion, which is univer- 
sal. Of the same description : 

A Certain sciences are classificatory ; 

U These sciences are Mineralogy, Botany, and Geology , 

A Mineralogy, Botany, and Zoology are classificatory. 

46*. Sir W. Hamilton has an ingenious mode of exhibiting all 
the possible forms of reasoning both in extension and comprehen- 
sion. The scheme shows 36 moods in each of the first three figures 
(the fourth is not allowed), or, in all, 108. Many of these moods 
would never occur (so it appears to us) in spontaneous thought, and 
arise from his giving Y, tj, and w, a place among propositions. Still 
the scheme is worthy of being looked at as exhibiting along with 
the forms arising in spontaneous thought, those that may be reached 
by immediate inferences. The Table, with the explanations, is 
taken from Thomson's Outlines of the Laws of Thought. (See p. 142.) 

In this Table M denotes the middle term ; and C and T the two 
terms of the conclusion. A colon (:) annexed to a term denotes that 
it is distributed, and a comma (,) that it is undistributed. Where 
the middle term has a : on the right side, and a , on the left, we 
understand that it is distributed when it is coupled in a judgment 
with the term on the right, and undistributed when coupled with 
the other. The syllogisms actually represented are all affirmatives, 
being twelve in each figure ; and the affirmative copula is the line 
— — , the thick end denoting the subject, and the thin the predicate, 
of extension. Thus C: ■- — , M would signify "All C is (some) M." 
In reading off the intension, the thin end denotes the subject. But 
from each affirmative can be formed two negative syllogisms, by 
making each of the premisses negative in turn. The negation is 
expressed by drawing a perpendicular stroke through the affirmative 
copula; thus n ■ . j.. ■ In the negative modes the distribution of 



142 HEA80N1NQ. 

Fig. I. Fig. n. Fig. III. 






ii. C, : M : , r C, : M : ■ , r C, ■■ : M : , r 



, iii. C, : M , : r C, — : m , : r C, ■ : M , ■ : r 



XXX 



iv. C: — — , M:— — , r C:- , M : ,r C: — ,M: 



v. C, — — : M , ■ , r C, — - — : M , , r C, ■ : M , , i 



XXX 



vi. C, , M : , r C, , M : , r C, — — , M : 






XXX 



viii. C, — : M : — : r C, : M : i : r C, : M : 



Ix. C : : M , : r C : : M , — : r C : . ; M , 



XXX 






xi. C : : M , , r C : : M , . , T C : — . : M , — — , r 



X X X 

xli. C, , M : — — : r C, . , M : ■ : I' C, — , M : : 1 

■ . 



MILL'S THEORY, 143 

terms will remain exactly the same as it was in the affirmatives 
from which they were respectively formed. The line beneath the 
three terms is the copula of the conclusion ; and in the second and 
third figures, as there may be two conclusions indifferently a 
line is also inserted above, to express the second of them. The mark 
s — y — ' under a mode denotes that when the premisses are converted, 
the syllogism is still in the same mode. But a X between two 
modes, signifies that when the premisses of either are converted, the 
syllogism passes into the other. The middle is said to be balanced 
when it is distributed in both premisses alike. The extremes, or terms 
of the conclusion, are balanced, when both alike are distributed or both 
undistributed ; unbalanced, when ©ne is and the other is not. Two 
propositions, or two modes, are balanced, when the distribution of 
terms is the same in both. A. 5. and ii. are balanced. B. The other 
modes are unbalanced. Of these, iii. and iv. are unbalanced in terms 
only, not in propositions ; the rest in both. 

4:7* The author of this treatise has commented elsewhere on Mr. J. 
S. Mill's theory of the reasoning process. " The ' really fundamental 
axiom of ratiocination,' as announced by him is, ' Things which co- 
exist with the same thing, co-exist with one another ; ' and ' a thing 
which co-exists with another thing, with which other a third thing 
does not co-exist, is not co-existent with that third thing.' But the 
phrase ' co-exist,' if limited to co-existence in respect of time or 
space, does not include most important cases of reasoning ; and if 
widened beyond this it becomes meaningless. When we argue that 
the man having committed murder deserves punishment, the pre- 
misses and conclusion have reference, not to space or time, but to 
far different relations. When we infer from A being equal to B, and 
B to C, that A is equal to C, we are not making affirmations about 
co-existence. In explanation, he tells us (Vol. I., p. 202, footnote, 6th 
ed.), 'the co-existence meant is that of being jointly attributes of the 
same subject.' This statement is still vague, and is not adequate, 
for it does not specify what is 'the same subject,' and it does not 
bring out that the attribution involves Extension : but it contains 
partial truth, and it has a meaning, which we can examine. 

This new Dictum gives him the following universal formula: 

Attribute A is a mark of attribute B ; 
A given object has the mark A; 
.•. The given object has the attribute B. 

But what does this first premiss mean when we translate it ffott' 



144 REASONING. 

abstractions into concrete realities ? As there cannot be an attri 
bute existing separately, or apart from objects, it must mean, ' What 
ever objects have the attribute A have the attribute B.' And wha' 
is this but the major premiss of the old syllogistic formula 1 The 
second premiss requires an explanation. "A given object has the 
mark A:" this object may be one object or a class of objects. Id 
order to give the formula a meaning, we must interpret it, ' What 
ever individual or class has the attribute A has the attribute B ; a 
given object or class C has the attribute A ; therefore it has the 
attribute B.' The new Dictum and new Syllogistic formula arejust 
bad versions of the old ones. I call them bad versions, for the 
phrase "co-exist" does not bring out the precise relation of the 
terms on which the thought proceeds ; and the phrase, " Attribute 
A," requires to be interpreted in order to have a relevant significa- 
tion." — Examination of Mr. J. 8. Mill's Philosophy. 

4z8* Some eminent mathematical logicians are seeking 
to introduce into Logic, reasoning founded on plurative 
judgments : 

Two-thirds of mankind are heathens ; 

Two-thirds of mankind live in Asia ; 
.•. Some who live in Asia are heathens. 

Now there is no doubt that this reasoning is valid 
But so also : 

Lias lies above Red Sandstone ; 
Red Sandstone lies above Coal ; 
.'. Lias lies above Coal. 

But all logicians allow that in the latter case there is a 
major premiss implied, that " when one stratum lies above 
a second, and that above a third, the first must be above 
the third "; and then the minor premiss becomes, " there 
is such a stratum (Lias), lying above a second stratum 
(Red Sandstone), which lies above a third (Coal)" ; and 
then the conclusion follows. It is the same in plurative, 
and indeed in all arithmetical reasoning, there must be a 
major premiss got from arithmetic, that is, from a region 
without and beyond pure discursive thought. 



CONDITIONAL REASONING. 145 



CONDITIONAL SEASONING. 

40' In this, one or both the premisses are conditional 
propositions. The common form is that in which the 
major premiss (so called) is a conditional, and the minor 
a categorical. 

ANTECEDENT. CONSEQUENT. 

If this man has consumption he shall die ; major premiss. 

He has consumption ; minor premiss. 

.-. He shall die. conclusion. 

This is called a Constructive Conditional Syllogism : it 
proceeds on the rule (modus ponens), Affirm the antecedent 
and we may affirm the consequent. In the Destructive form 
the rule (modus tollens) is, Deny the consequent and we may 
deny the antecedent. 

If this man has consumption he shall die ; 
He shall not die ; 
.•. He has not consumption. 

But we are not entitled by denying the antecedent to 
deny the consequent, or by affirming the consequent to 
affirm the antecedent ; for the consequent may follow 
from some other antecedent. We cannot, by denying 
that this man has consumption, deny that he shall die ; 
or by affirming that he shall die, that therefore he has 
consumption ; for he may die of some other disease. 
Hence arise two fallacies in conditional reasoning : one 
that of denying the antecedent and therefore denying the 
consequent ; the other that of affirming the consequent 
and therefore affirming the antecedent. 

So far for reasoning in which the major premiss has 
one or more concepts, and in which the proposition is 
attributive or the relation one of joint extension and com- 
prehension. But there are cases in which the notions are 
singular or abstract, and in which the proposition is 
10 



146 REASONING. 

equivalent, U ; and in these we can, from the denial of 
the antecedent deny the consequent, and from the affirm- 
ation of the consequent affirm the antecedent. " If Ho- 
mer wrote the Iliad he is the greatest poet in antiquity " 
From this we can infer not only (1) that as he wrote the 
Eiad he is the greatest poet in antiquity ; and (2) that he 
is not the greatest poet in antiquity if he did not write 
the Iliad ; but farther (3), that if he did not write the 
Iliad he is not the greatest poet in antiquity ; and (4) 
that as he is the greatest poet in antiquity, he must have 
written the Iliad. 

50. The common forms with a conditional major and 
categorical minor are : 

1) If A is B, B is C (major). 

Equivalent and attributive A is B .\ B is C. B is not C .". A is 

notB. 
Equivalent additional A is not B .-. B is not C. B is C .". A is B. 

(2) If A is B, C is D ; A is B .-. C is D. C is not D .-. A is not B. 

(3) If A is not B, C is not D ; C is D .-. A is B. 

(4) If A is not B, C is D ; A is not B .-. C is D. C is not D.\ Ais B. 

(5) IfAisnotB, CisnotD; A is not B .-. C is not D. CisD.\ AisB. 

(6) If A is B, either C is D, or F is G. 

A is B .-. either C is D, or P is G. Neither C is D, nor F is G, 
.: A is not B. 

(7) If either A is B, or C is D, either E is F, or G is H. 
Either A is B, or C is D .-. either E is F, or G is H. 
Neither E is F, nor G is H /. neither A is B, nor C is D. 

Other conclusions may be drawn when the terms are 
equivalent, but it is needless to formulize them. 

51. Reasoning, being all the while one and the same, 
will spontaneously take the conditional or categorical 
form according to the case to which it is applied. We 
reason and conclude that " a man guilty of murder should 
be punished." If we know that a particular man com- 
mitted the murder, the reasoning would take the categor- 
ical form, " This man, having committed murder, should 



CONDITIONAL REASONING 147 

be punished." We may not know, however, whether the 
man has committed the murder, and we simply assert 
that " this man, if guilty of murder, should be punished," 
thus declaring the validity of the consequence. But we 
come to know that he has committed the murder, and we 
apply the reasoning, and the form spontaneously assumed 
will be the categorical. 

52. There is a sense in which all reasoning is regarded by lo- 
gicians as hypothetical, that is, he does not, in looking at the valid- 
ity of reasoning, examine the truth of the premisses. Assuming 
them to be true, he inquires solely into the relation between them 
and the conclusion. But in Hypothetical Reasoning Proper, there is 
a hypothesis in the very enunciation of the argument. The relation 
of categorical and hypothetical reasoning is analogous to that be 
tween the original and derived propositions in Implied Judgments. 

33* All conditional reasoning can be reduced to cate- 
gorical form. This is accomplished by putting the major 
premiss in a new shape by immediate inference : as " the 
case of a man committing murder is a case in which he 
should be punished," or more simply : 

He who is guilty of murder should be punished ; 
This man is guilty of murder ; 
.•. He should be punished. 

When in conditional form, the reasoning is to be tried 
by the rules of conditionals ; when in categorical form by 
the rules of the syllogism. It will be found that the fal- 
lacy of denying the antecedent and thence denying the 
consequent, corresponds to illicit process of the major or 
negative premisses, or the introduction of more than three 
terms. In conditional form, " If this man has consump- 
tion he shall die ; he has not consumption ; therefore he 
shall not die," becomes categorically, "He who has con- 
sumption shall die ; this man has not consumption ; there- 
fore he shall not die " (illicit major). The fallacy of as- 
serting the consequent and thence inferring the antece- 
dent corresponds to the fallacy of undistributed middle or 



148 REASONING. 

negative premisses. With the same majors, " This man 
shall die, therefore he has consumption," is in conditional 
reasoning the fallacy of affirming the consequent, and in 
categorical of undistributed middle. It is evident from 
these considerations and examples, that conditional rea- 
soning is the same substantially in the relation of the 
terms as categorical, and that it is governed in thought 
by the principles expressed in the Dictum of Equivalence 
and the Dictum of Aristotle. 



DISJUNCTIVE EEASONBTG. 

54z. In it one premiss is a disjunctive proposition, and 
the other is categorical. The disjunctive proposition 
proceeds on the principle that the notion is divided into 
subordinate species, and is governed by the rules of Log- 
ical Division (P. I., § 58, 59) : that the species must make 
up the genus, and that the species must exclude one an- 
other. In it there are two or more judgments which 
cannot all be true, but one or some of which must. In 
the categorical premiss (called the minor) we make a 
predication as* to one or other of the species, and in the 
conclusion, we draw an inference as to the other or 
others : 

Lines are either straight or curved ; 

The line A B is not straight ; 
.*. It must be carved. 

Here we find " line " divided into two exclusive species 
we affirm that it is not in the one species and so infer it 
must be in the other. There is the same process when 
the members are three : 

The Apostles must either have been deceivers, or deceived, or thej 

spake the truth ; 
They were not deceivers nor deceived ; 
•. They spake the truth. 



DISJUNCTIVE REASONING. 149 

Or with four members : 

The season must have been spring, or summer, or autumn, 01 

winter ; 
It was winter ; 
.•. It could not have been spring, or summer, or autumn, 

A fallacy often creeps into disjunctive reasoning in con- 
sequence of the division in the disjunctive premiss not 
being exhaustive. Thus it is argued " either that all our 
ideas are had from experience, or that there are innate 
ideas." Then it is shown that " there are no innate ideas," 
i. e., that the child is not born with ideas ; and the con- 
clusion follows that " all our ideas are from experr 
ence." But there is a third supposition, which seems the 
true one, that " there are innate laws or principles in the 
mind, ready to be called forth by experience." "We have 
given other examples in treating of Logical Division, 
(P. I., § 58.) The detection of such fallacies requires us 
to look beyond Formal Logic, but Logic tells us where 
they lurk. 

55. The following are the principal forms (Fowler's 
Logic) : 

Either A is B, or C is D (major). 
(1) A is B .-. C is not D. (2) A is not B .-. C is D. 
(3) C is D .-. A is not B. (4) C is not D .-. A is B. 

Either A is B, or C is not D (major). 
(1) A is B .-. C is D. (2) A is not B .-. C is not D. 
(3) C is not D .-. A is not B. (4) C is D .-. A is B. 

Either A is B, or C is D, or E is F (major). 
(1) A is B .-. neither C is D, nor E is P. (2) A is not B .-. either 

is D, or E is F. 
(3) Neither C is D, nor E is F .-. A is B. (4) Either C is D, or E is 

F /. A is not B. 
(5) Either A is B, or C is D .-. E is not F, &c, &e. 

56. Disjunctive reasoning can be reduced to categor- 
ical in changing by immediate inference the disjunctive 
proposition according to the rule of logical division. 



150 REASONING. 

All lines not-straight are crooked , 
A B is not-straight ; 
•.It is crooked. 

This shows that ultimately disjunctive reasoning is 
founded on the same principle as categorical, that is, on 
the principle of subalternation of the species to the genus, 
implied both in logical division and in the Dictum of 
Aristotle. 

DILEMMA. 

S7. There are spontaneous exercises of thought in 
which we draw a conclusion from disjunctive premisses, 
or reach a disjunctive conclusion without determining 
which of the alternatives is to be preferred ; and in these 
the reasoning takes the form of a dilemma. In it we 
have a conditional premiss, in which either the antece- 
dent or consequent is disjunctive, and in the other pre- 
miss we make a predication in regard to the exclusive 
nature of the disjunctive in the premiss, and thence draw 
a conclusion. 

Major. If a man can help a thing he should not fret about it : if 

he cannot help a thing he should not fret about it 
Minor. But he can either help a thing or not help it ; 
.*. He should not fret about it. 

He who opposes this must set himself against one or 
other of the alternatives — must, as it is said, choose his 
horn, and if the alternative is exhaustive, he will be trans- 
fixed by either. If a dilemma is accurate in form, the 
conclusion follows, and the only way of meeting it is by 
showing that the alternatives in the premisses are not 
exhaustive — that there may be another supposition. 

If that narrative be true you must believe it ; if it be false you 

must disbelieve it ; 
But it must either be true or false ; 
. You must either believe it, or not believe it. 



DILEMMA. 151 

But there may be a third supposition, that it is partly 
true and partly false. The rules are (1), The antecedent 
being affirmed, either disjunctively or not, as the case 
may be, the consequent must be admitted; (2) The conse- 
quent being denied, either disjunctively or not, the ante- 
cedent must be denied. 

58. (1) There are cases in which the first premins 
consists of one antecedent and several consequents. The 
conclusion is destructive. 

If A is B, C is D, and E is F ; 
But either C is not D, or E is not F ; 
.*. A is not B. 

(2) In which the major consists of several antecedents 
and one consequent ; and we draw the common conse- 
quent in the conclusion. The argument is constructive • 

If A is B, or if C is D, E is F ; 
But either A is B, or C is D ; 
.-. E is F. 

(3) In which each of the antecedents has a different 
consequent, and we can draw the consequent only disjunc- 
tively. The argument may be constructive or destructive : 

Major. If A is B, C is D, and if E is F, G is H ; 
Minor. But either A is B, or E is F ; 

.-. Either C is D, or G is H. 
Minor. But either C is not D, or G is not H ; 

.-. Either A is not B, or E is not F. 

59. There may be Trilemma or a Tetralemma, &c, when tb.6 
number of antecedents or consequents, one or both, is three, four 
&c. Trilemma. If the universe is not the best possible, we must 
suppose that God did not know a better, or that he could not make 
a better, or that he did not desire a better. The first supposition 
cannot be true (for it is inconsistent with His wisdom) ; and the 
second (because it limits His power) ; and the third (because against 
His goodness) ; therefore the universe must be the best possible. 

60. A Dilemma being a condition a] with a disjunctive 
proposition, may be reduced to categorical syllogistic 
form, like conditionals and disjunctives. 



152 REASONING. 



CHAINS OF REASONING— THE SORITES. 

01. Prosyllogism and Episyllogism. Hitherto we have 
been considering single arguments. But ratiocination 
is commonly conducted in a train, and the single 
argument has a connection with what goes before and 
with what follows. The major or minor premiss, one or 
both, of any syllogism, may have been established by a 
previous act of reasoning, which in relation to that syl- 
logism is called a Prosyllogism. Or a syllogism may be 
employed to establish a position to be used as a premiss 
in a subsequent syllogism called an Episyllogism. The 
conclusion in the Prosyllogism is a premiss to the syUo- 
gism which it precedes ; the Episyllogism uses the con- 
clusion of the syllogism which goes before as a premiss. 
It is evident that the same syllogism may be a Pro-syllo- 
gism in one connection, and an Epi-syUogism in another. 

Pro-Syllogism. He who administers arsenic administers poison ; 

The prisoner administered arsenic ; 
. . The prisoner administered poison. 
Given Syllogism. He who administers poison is guilty of murder , 
The prisoner administered poison ; 
.•. He is guilty of murder. 
Epi-Syllogism. He who is guilty of murder should bo executed , 

The prisoner is guilty of murder ; 
.•. He should be executed. 

This may become a Prosyllogism to a farther act of 
reasoning : 

He who is to be executed should not be executed in publie ; 
This man is to be executed ; 
.•. He should not be executed in public. 

This may be taken as an example of a chain of reason- 
ing. It is not to be understood that in spontaneous 
thought, the mind constructs the reasoning into syllo 



CHAINS OF REASONING, ETC. 153 

gisms. It is enough, that it perceives the relations in- 
volved in the terms. The formal unfolding of the rela- 
tions is left to the logician. 

02. Logicians have drawn the form of one of these 
chained trains of reasoning, and call it the Sorites (from 
acopoc, a heap — the Germans call it chain argument, Ket- 
tenschluss) : — The prisoner administered arsenic to the 
man who died ; he who administers arsenic administers 
poison ; he who administers poison is guilty of murder ; 
he who is guilty of murder should be executed ; he who 
is executed should not be executed in public ; .'. the pris- 
oner should not be executed in public. The Sorites con- 
sists of a series of propositions, the predicate of each be- ' 
coming the subject of the one following, till in the last - 
step the predicate of the last is affirmed or denied of the 
subject of the first, which is the conclusion. In the pro- 
cess there are as many middle terms as there are prop- 
ositions between the first and the last ; and the mind in 
reasoning sees the connection between these middles and 
the other terms, and thus passes on from the first pre- 
miss to the final conclusion. The Dictum of Aristotle 
slightly modified, is the regulating principle. " Whatever 
is affirmed or denied of a whole class, may be affirmed or 
denied of whatever is comprehended in any class that is 
wholly comprehended in that class," — the words in Italics 
being an addition. In the Sorites the first proposition, 
and that alone (with the last), can be particular ; because 
in the first figure the minor may be particular but not the 
major (§ 29), and all the other propositions on to the con- 
clusion are major premisses. There can be one and only 
one negative premiss, and that the last ; for if any others 
were negative, one of the syllogisms would have a nega- 
tive premiss, which cannot be in the first figure. 

03. The reasoning is perfectly valid, but we may in 
the way of testing it, and to show that this form oJ 



154 REASONING. 

reasoning is founded on the same principle as the syllo- 
gism, draw out the process in a series of syllogisms. 
These will all be in the first figure ; the same in number 
as the middle terms ; and the first will have for its major 
premiss the second proposition of the Sorites, and for its 
minor the first. Syllogisms thus drawn out, will take the 
form of syllogism, pro-syllogism, and epi-syllogism, given 
above : 

The form is, All (or some) A is B ; 

All B is C ; 

All C is D; 

All (or no) D is E ; 
.-. All (or some) A is (or is not) E. 

Keduced to syllogisms : 

All B is C ; All C is D ; All (or no) D is E ; 

All (or some) A is B ; All (or some) A is C ; All (or some) A is D ; 
.*. All (or some) A is C. .\ All (or some) A is D. .'. ALL (or some) A is (01 

is not) E. 

Trie Sorites may take another form called Goclenian (from Gocle- 
nius who noticed it). The subject of each premiss becomes the 
predicate of the next ; the conclusion predicates the first predi- 
cate of the last subject ; the first premiss only cau be negative and 
the last particular. When expanded into syllogisms the conclusion 
of each becomes the major premiss of the next. The form is : 
All (or no) E is F ; All B is C ; 

All D is E ; All (or some) A is B ; 

All C is D ; .*. All (or some) A is (or is not) F. 

He who is executed should not be executed in public ; he who is 
guilty of murder should be executed ; he who administers poison is 
guilty of murder ; and he who administers arsenic administers 
poison ; the prisoner administered arsenic ; therefore the prisoner 
should be executed, but not in public. These two forms differ from 
each other only as a syllogism with the major premiss put first, and 
the minor premiss second, differs from a syllogism with the minor 
premiss put first and the major last (see § 18). A series of Con- 
ditional arguments may in the same way be abridged into a Sorites 
[f A is B C is "D ; if C is D, E is F. But A is B .-. E is F. 



REMARKS ON REASONING PROCESS. 155 



GENERAL REMARKS ON THE REASONING PROCESS. 

64. We have seen that in all reasoning there is in- 
volved a comparison of two terms by means of a third, 
and that when the process is fully unfolded, there will be 
three propositions, that is, two premisses and a conclu- 
sion. The question arises, whence do we get the premis- 
ses ? The answer is, that they may be obtained either by 
intuition or by experience. First there are premisses 
gained by an immediate intuition of objects. It is thus 
that I know that these two parallel lines will not meet 
however prolonged ; that these two straight lines cannot 
enclose a space ; that this deed of ingratitude to God and 
cruelty to man is a sin. We reach these truths by no 
process of inference ; we perceive them to be true on the 
bare contemplation of the objects. But a far greater 
number of premisses are attained by ordinary obser- 
vation — in the case of general truths by a gathered obser- 
vation. It is thus we know that fire burns, that all bodies 
attract other bodies, that plants and animals need nourish- 
ment, and that animals feed on other organized matter. 

65. This gathered observation may be made by the 
individual for himself, or by the combined experience of 
others. Of these, the individual experience, so far as 
it goes, is by far the more valuable ; as with the results 
we have the processes which guide and restrain in the 
application of the general maxim. It is for this reason 
that a mere school or book learning can never serve the 
ends of a practical education ; and that a dear-bought 
personal experience is often worth all the labor and suf- 
fering which may have been expended in gaining it. But 
on the other hand, individual observation, however en- 
larged, must always be limited, and unless widened by 
intercourse with mankind and by reading, tends to be* 



156 REA80N1JS(*. 

come narrow and exclusive. By far the greater part of any 
man's knowledge is derived from the experience of others, 
and is conveyed to him by oral instruction and hooks ; 
and the most valuable jjart consists in nice distinctions 
and scientific laws, some of which embody the results of 
the thoughts of the greatest men who have appeared on 
our earth, and of a hundred generations. 

00* Some of these have been written out and pro- 
claimed to the world ; such, for instance, are ascertained 
natural laws, as the three laws of motion, the classifications 
of natural history, the chemical affinities of bodies, and 
certain laws of the mind, such as those of the logical pro- 
cesses, of intuition, and the association of ideas. It is one 
of the advantages which the modern reasoner has over 
the ancient, that he has provided for him and placed at 
his disposal, an immense number and variety of general 
principles handed down from the ages precedent. Others 
of the published maxims are of a moral and practical 
nature, such as proverbs and wise saws handed down 
from father to son and from one generation to another, 
as " Evil communications corrupt good manners," " Sec- 
ond thoughts are best." Others of the maxims have not 
been embodied in words and never will be. For example, 
you have discovered of a certain man that you can trust him, 
and you confide in his statements, and coidd place your 
property in his hands. Or, you have found of a certain 
look and manner, which you know but could not describe, 
that they are signs of deceit and dishonesty. Such media 
axiomata, as Bacon calls them, equally removed from high 
generalizations and minute particulars, are most useful 
of all in the arts and the practical business of life. And 
observe wherein lies their utility. They form, as we shall 
immediately see, the major premisses in that reasoning 
which the mind is ever conducting in regard to the cases 
that cast up — these cases supplying the minors. One 



REMARKS ON REASONING PROCESS. 157 

grand use of education in the higher sense of the term, 
of travel, and of an acquaintance with the world, is to 
supply such majors for continual use and application in 
the varied circumstances of life. 

07. Many of the maxims are absolutely certain. Such 
are established scientific laws, as those of chemical affin- 
ity, of physiology, and psychology. Such are also aL 
moral maxims, as that it is wrong to lie, to thieve, tc 
kill. In other cases, the maxim is true only in most 
cases. For example, the rule that netted-leaved plants 
are exogenous is true only as to most plants ; foi 
there is a tribe called dictyogens by Lindley, which have 
netted-leaves and yet are endogenous. The general ob- 
servation that solanacese are poisonous, has a still greater 
number of exceptions — for the potato is a solanaceous 
plant ; and all that such a rule can do is to guard 
against eating the flowers or berries of this tribe of 
plants when they come in our way. Of this character 
are the loose maxims which float in the world as to races 
and nations. Acting on them we are commonly right, 
while we should greatly err if we insisted on applying 
them rigidly. " One of themselves, even a prophet of 
their own, said, the Cretans are always liars, evil beasts, 
slow bellies," " Frenchmen are lively," " The Irish are 
witty," " The Scotch are cautious." 

08. When all the new steps in the reasoning process 
are seen to be true intuitively, we have what is called 
Demonstration (a-rrodet&g). The fittest example is to be 
found in Mathematics. Here we start with things defined, 
that is, with points, lines, squares, ellipses, &c, and look- 
ing to these things, on the bare contemplation of them, 
we discover certain truths regarding them. This is what 
is to be understood by intuitive truths — truths seen on 
the bare inspection of the things. Having thus obtained 
certain truths, we compare two truths by means of a 



158 REASONING. 

third — which is reasoning — and rise to farther and far- 
ther truths. Finding that the line AB = the line C D, 
and C D = E F, we conclude that A B = E F. The things 
we thus compare are all abstracts, and the notions are all 
distributed both in the subject and the predicate. This 
kind of reasoning all falls under the head in which the 
law of Equivalence is the regulating principle. We may 
arrange the terms as we please as subject and predicate 
in the proposition, and the propositions as we please in 
the syllogism — there being, properly speaking, no major 
and no minor. We do not require to announce a gene- 
ral principle, as that things which are equal to the same 
things are equal to one another ; on the bare contem- 
plation of A B and E F being equal to G D, we conclude 
them to be equal to one another. This reasoning is 
also found to a limited extent in Formal Logic, as when 
we draw the rules of the syllogism (§ 20-23) and the spe- 
cial rules of the figures (§ 29-34) from the Dictum of Aris- 
totle. It cannot, however, be employed in any of those 
departments of knowledge in which we deal with scat- 
tered facts. In such branches, the only available method 
is that of Induction — a subject which does not fall under 
Formal Logic, but that Secondary department which 
treats of discursive thought as applied to certain classes 
of objects. 

SOo When the evidence is gained from a gathered ex- 
perience, it is called Experiential, also Probable, and 
Moral. It is of importance that we should know the 
difference between this and Demonstrative or Apodictive 
evidence. (1) The essential distinction is that the one 
is derived exclusively from intuition, and the other partly 
or wholly from experience. In order to discover th<. truth, 
the mind in the former case looks simply at the object ; 
whereas in the latter there is need of observation, com- 
monly of observation upon observation. There is no 



REMARKS ON REASONING PROCESS. 159 

ueed of trial in order to convince us that two parallel 
lines will never meet ; the truth is discovered at once by 
the bare contemplation of parallel lines. But we cannot 
by thus inspecting the things say whether the planets do 
or do not move in ellipses, whether the earth is or is not 
hot in the centre. "A clever man shut up alone and 
allowed an unlimited time, might reason out for himself 
all the truths of mathematics, by proceeding from those 
simple notions of space and number of which he cannot 
divest himself without ceasing to think ; but he could 
never tell by any effort of reasoning what would become 
of a lump of sugar in water, or what impression would be 
produced on his eye by mixing the colors yellow and 
blue." (Sir J. Herschel.) (2) The one does not, the other 
does, admit of degrees. Demonstration does not allow of 
degrees. Every one proposition so substantiated, is as 
certain as any other, as every other. Nor can we add to 
the evidence of a proposition demonstrated. That the 
opposite angles formed by the crossing of two straight 
lines are equal, this cannot be rendered more certain by 
any addition of proof. It is different with observational 
evidence which admits of all degrees of certainty. That 
it will rain to-morrow is a vastly more uncertain propo- 
sition than that the sun will rise to-morrow. This kind of 
evidence may have additions made to it ; the probability 
of there being rain may be increased by the fall of the 
barometer and the threatening aspect of the sky. It may 
rise at last to moral certainty, which ought to carry our 
full conviction and lead to corresponding action. (3) In 
the one there is not, in the other there commonly is, a 
balancing of seemingly opposite proofs. In Demonstra- 
tion there never is anything contrary, even in appearance, 
to what has been established. But in Probable evidence 
there is often one fact or argument which seems to in- 
cline one way, and another which seems to tend the 



160 HEASOxVIWG. 

other way ; and in order to arrive at a satisfactory conclu- 
sion, we must look at both, and give to each its proper 
weight. What a number of considerations require to be 
estimated before a merchant makes an extensive purchase 
of certain goods ; before a statesman proposes a measure 
with far-reaching consequences ; before a general ventures 
on a perilous campaign ! The most useful of all kinds 
of practical sagacity is that which enables a man, in 
the midst of complicated circumstances, to determine on 
which side the balance of probability lies. (4) The one 
does not, the other does, involve responsibility. There 
is no sort of accountability attaching to intuitive evidence ; 
a man must believe it, whether he will or not. We have 
no credit, or the reverse, in believing that if we take equals 
from unequals that the remainders are unequals ; or that 
the angles at the basis of an isosceles triangle are equal 
to one another. As soon as any one understands these 
propositions and the evidence advanced in their behalf — 
if they need proof — he is obliged to yield his assent to 
them. It is different with Experiential Evidence. A man 
may or may not listen to it ; he may, but he also may not, 
act upon it. There is room here for the influence of a 
spirit of candor, or for the opposite temper of prejDosses- 
sion and prejudice. It is on this account, that experien- 
tial evidence is often called Moral, because it is possible 
for us either to attend to it or not to attend to it, and the 
act to be morally right or morally wrong. 

tO. It is vain to expect Demonstration in every line of 
inquiry. Demonstration is confined to a limited class of 
objects, and these characterized by their simple and ab- 
stract nature. In most of the sciences it is not available ; 
it cannot be had in chemistry, in natural history, in psy- 
chology, in political economy. In the practical affairs of 
life no man looks for it. If a man's house is on fire, he 
will proceed to pour water upon it, though it cannot be 



REMARKS ON REASONING PROCESS. 161 

demonstrated in the technical sense of the term, that 
water will quench the flame. The evidence adduced in 
behalf of the existence of God, of the immortality of the 
soul, of a day of judgment, and of the truth of the Chris- 
tian religion, is all of this moral character. It is addressed 
to an understanding capable of weighing it, and a heart 
supposed to be ready to receive it. There may be excel- 
lence implied in the faith that receives it ; and guilt 
involved in the perverseness which rejects it.* 

71> To return from this seeming digression. It is to 
be observed that all reasoning proceeding on experiential 
evidence falls under the Dictum of Aristotle, and in order 
to its validity we must have a major as well as a minoi 
premiss. The major may not always be expressed ; the 
argument often takes the form that is vulgarly called an 
Enthymeme, that is, with one premiss suppressed. But 
one reason for its being so often unnoticed is that we are 
so familiar with it ; and whether expressed or not, it is" in 
all cases implied, and we proceed upon it in our reason- 
ings. 

72. It has been disputed whether there is reasoning 
involved in the Inductive Method of inquiry, by which all 
discoveries have been made in physical and mental 
science. In that method two steps are involved : one is 
the gathering of the facts ; the other the gathering of the 
law out of the facts. In the former there may be no 
special exercise of ratiocination ; but in the latter there 
is ; we proceed from something given to something de- 
rived from it, from the facts to the law of the facts. And 

* " I receive mathematics as the most sublime and useful science as long as 
they are applied in their proper place ; but I cannot commend the misuse of 
them in matters which do not belong to their sphere ; and in which, noble 
science as they are, they seem to be mere nonsense ; as if, forsooth, things only 
exist when they can be mathematically demonstrated. It would be foolish for 
a man not to believe in his mistress's love because she could not prove it to him 
mathematically. She can mathematically prove her dowry, but not her love."- 
Goethb's Conversations with Eckermann. 

11 



162 REASONING. 

this reasoning can be reduced to syllogistic form. In the 
inference there are two things involved ; one is the facts 
gathered, and the other some general principle on which 
we proceed in reaching the law from the facts. Attempts 
have been made to enunciate the principles which entitle 
us to rise from the particulars to the laws and causes. 
The first systematic attempt was made by Bacon, who 
enumerated a number of Prerogatives of Instances (Pre- 
rogativse Instantiarum), which enable us to proceed 
from the facts to what he called axioms, causes, and 
forms. In this past age these have taken a better form 
in what are called Canons of Induction. Now these Pre- 
rogatives of Instances, or Canons of Induction, are in 
fact the major premisses, while the observed facts consti- 
tute the minor premisses in the process by which we rise 
from the facts to the law. To give an example. The an- 
cients referred the rising of water in a pump, and of mer- 
cury in a tube, to nature's horror of a vacuum. Toricelli 
and Pascal referred it to the weight of the atmosphere. 
The case was decided by taking a barometer to the top of 
a mountain, when it was found that the mercury de- 
scended as the instrument was carried up to a higher 
elevation. One of Bacon's Prerogatives of Instances 
guarantees the process, what he calls the Experimentum 
Crucis : When there are two rival theories, let us produce 
a phenomenon which can be explained by the one and not 
by the other, and it will prove the truth of the theory 
which furnishes the explanation. This constitutes the 
major premiss, and the minor premiss is the fact that the 
mercury sinks as the atmosphere becomes lighter, — a fact 
which cannot be explained on the theory of nature's hor- 
ror of a vacuum, but can on the other. The process may 
be unfolded still more clearly by that Canon of Induction 
called the Method of Difference. " If in comparing one 
ease in which the effect takes place, and another in which 



REMARKS ON REASONING PROCESS. 1G3 

it does not take place, we find the latter to have every an- 
tecedent in common with the former except one, that one 
circumstance is the cause of the former, or at least, part of 
the cause of it." This is the major premiss in the argu- 
ment. The minor is, that at the foot of the mountain 
where the atmosphere was heavy the mercury was high, 
while it was low at the top where the atmosphere was 
light. The two together guarantee the conclusion that 
the weight of the atmosphere is the cause, or part of the 
cause, of the rise of the mercury. 

73, The best exposition of the Canons of Induction is by Mr. 
Mill (Logic, B. III., c. viii.). He states and illustrates five : — that ol 
the Method of Agreement, of the Method of Difference, of the Joint 
Method of Agreement and Difference, of the Method of Residues, 
and of Concomitant Variations. But he does not perceive that 
their Canons are the major premiss, while the facts are the minor 
premiss, in the process by which we reason from the facts to the 
law. We are prevented from enlarging on this subject only by the 
circumstance that it would carry us into Particular Logic. It is 
enough to show here how the reasoning involved in Induction can 
be reduced to syllogistic form. 

74. When the premisses are only probably true, the 
conclusion is also only probably true. " Bash actions lead 
to evil consequences," is true only in a general way — 
there are cases in which rash deeds have led to brilliant 
results. But in dealing with such general maxims, we 
are not to allow to the conclusion a certainty not found 
in the premisses — to use a graphic illustration of Whate- 
ly's — " The chain is not stronger than its weakest part." 
It is evident that if both the premisses in an argument, 
and still more if all the premisses in a chain of argument, 
be only probably true, the conclusion is more uncertain 
than any one of them. If a story has reached us through 
a number of persons detailing it the one to the other, it 
may come in the end to be very doubtful, even though 
each narrator be probably trustworthy. It is thus that 
events, handed down from age to age by tradition, be 



164 REASONING. 

come in the end very uncertain — the stream may at first 
have been pure, but it receives a polluting mixture in 
every region through which it passes. Sometimes we 
can, in a loose way, numerically estimate the probability 
attaching to each premiss in the chain of proof, and then 
we can state the conclusion numerically. The incident, 
we may suppose, has reached us through three persons : 
one trustworthy, and we value his testimony at T 9 , re- 
garding 1 as absolute certainty ; the testimony of another 
we reckon f , and of the other i ; the probability of the 
story being true is now T 9 x f x ! = |^ ; and we see that 
the story is more likely to be false than true. The suc- 
cess of a scheme depends, we may suppose, on the com- 
bined character and ability and wisdom of the person who 
manages it. His character we estimate y 9 ^ ; his ability, 
y 7 ^ ; and his wisdom, f V) ; the probability of his success 
will be y 9 ^ x T 7 o x T % = y 3 o 7 o 8 o5 or the scheme is more likely 
to fail than to succeed. It is seldom that in the practical 
affairs of life we can get numerical estimates of any value. 
When, however, the data are derived from such occur- 
rences as the average number of deaths taking place an- 
nually among a definite number of persons, and of fires 
occurring in a certain description of property, Insurance 
Companies can make calculations which are rigidly cor- 
rect as to averages. But in all such cases the calculation 
belongs rather to the arithmetician than the logician. 
The shrewd man of the world, without expressing his 
premisses or conclusion in numbers, can commonly ob- 
tain sufficient data to enable him to reason and reach a 
sound conclusion, as to the side on which the probability 
lies, in departments falling under his habitual notice. He 
may err in regard to a given proposal made to him, and 
lose much by acting or not acting ; but in the long run 
he will be found in acting on the rules (majors) which he 
has laid down for himself, to have acted judiciously. He 



REMARKS ON REASONING PROCESS 165 

who proceeds habitually on such principles as that "rash 
actions are to be avoided," " honesty is the best policy," 
will be found in the end to have acted a prudent part in 
this world. Swayed by other and moral principles, he 
will be found to have acted a good and a geneious part. 

7«>. When there is a concurrence of evidence towards 
a particular point, the conclusion is more probable than 
any of the premisses. An incident is detailed to us by three 
independent witnesses known to us to be trustworthy, and 
we have now quite as certain proof as is to be had in this 
world. We estimate the probability of each of them 
speaking the truth as T % ; this makes the probability of 
each of them speaking falsely as only T ^ 3 and the proba- 
bility of the three concurring in a falsehood as fa x fa x 
fa, or only T fa „. Of this description is the evidence in be- 
half of the great doctrines of natural and revealed religion. 
Thus in behalf of the existence of God, we have the argu- 
ment from the evident design in the structure and adap- 
tations of animal and plant, the native disposition to trace 
the seen effects to their unseen cause, and the conscience 
or law in the heart pointing to a lawgiver. In favor of 
the Christian religion we have the deposition of witnesses 
that Jesus performed miracles and rose from the dead ; 
and we have the character of Jesus and the doctrines he 
taught, the spirit he inculcated and the precepts he en- 
joined. Evidence of this kind is called Cumulative, and 
may amount, as in the cases just mentioned, to the highest 
moral certainty. There is still, to be sure, a bare possi- 
bility of error, but it is as one to a thousand, a million, or 
a million millions. Only diseased minds will allow them- 
selves to dwell on it — only the fool will say in his heart. 
There is no God. But healthy minds will brush it aside, 
will in fact not feel it in the view of the overwhelming 
evidence on the other side. 

¥6. When there is a concurrence of facts towards a 



166 REASONING. 

conclusion, the point may be regarded as established when 
no one of the proofs is itself sufficient. This is what is 
called Circumstantial Evidence. A murder has been 
committed, a person is charged with the crime, and the 
proof runs as follows : 

The murderer may very likely have blood on his clothes ; 

This man had blood upon his clothes ; 
. . He is the murderer. 

The murderer must have been prowling about the premises; 

This man was prowling about the premises ; 
'. He is the murderer. 

The murderer will have some of the goods of the murdered man 

This man had some of the goods of the murdered man ; 
•. He is the murderer. 

No one of these arguments is in itself conclusive. The 
syllogisms are all in the second figure ; the premisses are 
both affirmative ; in neither is the middle term distribu- 
ted, and so no conclusion can be drawn. But by such 
considerations we reach a general major premiss, that the 
person thus found with blood on his clothes, thus seen 
prowling about the premises, and caught with the prop- 
erty of the murdered man in his possession, must be the 
murderer, and the conclusion follows syllogistically. 

77. Whence the rapidity and the unreflective nature of 
the process ? It is acknowledged by all logicians, that in 
spontaneous reasoning we have not before us consciously 
the distinction between major, minor, and middle, the 
moods and the figures of the syllogism. I hold, indeed, 
that in all reasoning, the mind has before it the terms, and 
perceives the relations between them ; but having this, 
it proceeds with amazing quickness and without analyz- 
ing or even reflecting on the process. This rapidity pro- 
ceeds from the laws of the association of ideas. These 
laws are those of Coexistence and Correlation. Things 
which have been together in the mind tend to suggest 
each other, as do also things that are related, say by re- 



REMARKS ON REASONING PROCESS. 1G7 

semblance, or means and end, or by cause and effect. Now 
in subjects with which we are familiar, we have laid up an 
immense store of such associations, partly by the things 
having been brought together in our experience, and 
partly by our being ever called on to notice relations. 
What a number of such associations are formed in the 
mind of the mathematician, the mechanic, the politician, 
and the student of the fine arts, each in his own depart- 
ment. And when he is meditating on any one topic, his 
thoughts flow on with amazing speed from one point to 
another. In this flow the terms of an argument or a 
train of reasoning come up, and he perceives the relations 
between them, and goes on from premiss to conclusion, 
and from one conclusion to a farther. Meanwhile he 
might be quite incapable of unfolding the process, or 
even of recalling the steps. At the same time it is ever to 
be understood that the train of ideas raised by association 
does not amount to reasoning. I believe that much of 
what is called reasoning in brutes, and even among chil- 
dren, proceeds from mere association. When the burnt 
child, and we may add the burnt dog, dreads the fire, it 
is from the mere law of coexistence. All their lives men 
are, more or less, under the influence of mere association, 
in cases in which we imagine them to be reasoning. They 
are led, not by a concatenated train of argument, but by 
mere impulse — as it is said, that is, by the suggestion that 
comes up. Hence the mistakes into which they are ever 
falling — mistakes not to be referred to the reasoning 
power. In all judgment, and in reasoning as implying 
judgment, there is a perception of the relations of the 
notions to each other ; and it is only thus we can reach a 
sound and safe conclusion. Association is to be allowed 
to aid us as an assistant, and to suggest terms for com- 
parison. But above it, as a master, there is to be an 
understanding to judge of the relations of the terms thus 



168 REASONING. 

brought before the mind ; not that we should adopt them 
or follow them, but that we should judge of them, and 
believe and act accordingly. 

78. In what sense are the truths reached by the rea- 
soning process new truths, and in what sense old truths ? 
They are old truths, inasmuch as they all depend upon, 
and are derived from, the truths with which the mind has 
started in the reasoning process. That this man will die, 
may depend on two other truths, that he has consump- 
tion, and that consumption produces death. That man 
will have to appear before the Judgment-seat, may depend 
on other truths, as that he is a moral being, possessing 
intelligence, conscience, and free will. The truths of the 
sixth book of Euclid are all obtained from the definitions, 
axioms, postulates assumed at the beginning, and from 
the reasonings of the first five books. But in another and 
an important sense they are new truths. They are not 
truths at all to us, till they are reasoned out ; they may 
not be known to us till they have been unfolded by 
the reasoning process. There are truths, especially in 
morals, but also in the fine arts, in geometry itself, and 
indeed in every department of knowledge, thus bursting 
upon us with all the freshness of novelty, because in fact 
they are now brought out by us for the first time, from 
premisses — it may be known to us for years. Such 
truths, it is often said, come to us by intuition ; but in fact 
they are obtained by a rapid reasoning process aided by 
association ; and we forget the steps we have taken in 
climbing, in the joy we experience because we have 
gained the height. 



FALLACIES. 169 



FALLACIES. 

70. A fallacy is defined " any unsound mode of argu- 
ing, which appears to demand our conviction and to be 
decisive of the question in hand, when in fairness it is 
not." Its genus is " any unsound mode of arguing ; " but 
every unsound mode of arguing is not a fallacy ; it is so 
only when " it seems to demand our conviction and to be 
decisive of the question in hand when " — we prefer saying 
— " it is not according to the laws of thought." In order to 
its being a fallacy, it is not needful that it should be stu- 
diously constructed for deceitful purposes. The man who 
uses it may himself be deceived by it ; or more frequently 
he has first been deceived by the influence of selfishness 
or passion, and " the wish becomes father of the thought," 
and the argument occurs to him and he advances it in his 
justification. Some logicians call a fallacy a Paralogism, 
wLen the man who employs it is deceived by it, and a 
Sophism when, being aware of its unsoundness, he uses 
it to deceive others. We need to be warned not only 
against the sophistry of designing men, but against the 
fallacies laid in our way by persons who believe what they 
say ; and, as still more dangerous, against those which 
originate in thoughts that favor our own selfish and 
crooked aims. 

80. In order to avoid all seeming exaggeration, we 
may state precisely what Logic cannot do, and what it 
can do, in the way of preventing us from being led astray 
by fallacious reasoning. It should be allowed at once 
that the best safeguard against error of every kind, is to 
be found in a sincere desire to discover the truth, which 
keeps the mind open to facts and arguments from what- 
ever quarter they come — " When the eye is single the whole 
body s full of light." Without this, no dialectic skill can 



170 REASONIM*. 

protect us from so insidious a foe as a deceitful heart. It 
may be farther admitted that native shrewdness can de- 
tect fallacies without the aid of logical rules. But freely 
granting all this, it may yet be maintained that many valu- 
able practical as well as scientific ends are to be gained 
by an acquaintance with logical principles and the viola- 
tions of them. It is most important, for the guidance of 
our thoughts, that we should know what are the essential 
steps involved in inference ; that we should be aware, for 
example, that there are always three terms, and a com- 
parison of two of these by the third ; and that in most 
reasoning there is a major premiss implied in the form of a 
general principle. By a logical training the mind is led to 
look keenly into the meaning of terms and the relation of 
terms one to another, to place the case fairly before it, to 
sift the proof which may be proffered, and to determine 
how far it is fitted to support the conclusion. How use- 
ful, too, to know what are the common forms of invalid 
reasoning, to be aware of the places where error lurks, that 
so we may be on our guard against its insidious attacks, 
or ready if need be to seek it out, and expose it to view 
and hunt it to death. By such a discipline the mind may 
acquire a habit which will lead it spontaneously to reason 
accurately, and gender a spirit of penetration, scrutiny, and 
caution, which will save it from being carried along by im- 
pulse, by plausible statement and clap-trap oratory. We 
find the correct speaker and writer coming to speak and 
write accurately without construing his sentences, but it is 
because he has previously studied grammar ; and the arith- 
metician makes his calculations without referring to rules, 
because the habit has become part of his nature. In like 
manner the correct thinker can conduct a long chain of 
ratiocination, without thinking of syllogistic formulee, but 
all the while the skill may be the result of logical train- 
ing, and there may be throughout an unconscious use of 



fallacies. 171 

the principles of reasoning. And just as an author when 
a dispute arises about his language, is obliged to resort 
to the rules of grammatical construction, and as the mer- 
chant's clerk when his accounts will not balance has to 
fall back on arithmetical rules to correct his blunders, so 
the reasoner may find it convenient when he hag any 
cause to doubt of his own arguments, or to dispute those 
of his neighbor, to have logical rules ready for applica- 
tion. In this way, any one who has a sincere desire to 
discover the truth, may be guided aright in his own cogi- 
tations, and kept from aberrations on cither side, and 
enabled to use any natural shrewdness which God mav 
have given him, in detecting the sophistries laid in his 
way by others. 

81. Psychology can explain how the heart sways the head. In 
all judgment, immediate or mediate, there is comparison ; the com 
parison of objects, two or more, represented to the intelligence and 
apprehended by it. But the representation may be a misrepresen- 
tation, the apprehension a mistaken one, and the judgment become 
in consequence a perverted one. A prejudiced heart presents a par- 
tial, an exaggerated, a distorted case to the judicial power. This is 
effected through the influence of the will on the train of association. 
We have already noticed the fact (§ 76) that while reasoning is not 
the same as the association of ideas, it is yet greatly dependent on 
it. It is by the laws of the succession of our ideas that the notions 
compared are suggested. Now the will has a direct and an indirect 
power over the train of thought and feeling. It has a direct power 
in retaining the present idea, for as long as the will to retain it 
exists, it keeps the idea before the mind ; and it is apt to detain 
oniy what pleases and gratifies vanity, pride, and passion, and it 
turns away from all that would reprove or humble. And then it 
has a more important indirect influence. In detaining the present, 
it collects around it a great many other thoughts connected with it 
by the laws of suggestion, say by the law of co-existence, or the law 
of correlation. In doing this, it calls into operation certain second 
ary laws, such as when we bestow a great amount of energy of any 
kind — say of thought, feeling, or attention — on any object, it will 
come up more frequently before the mind. The heart thus sends up 
to the head an immense number of ideas, all of one complexion ; and 



172 REASONING. 

the will seizes eagerly on those that please it, and as it lodges then? 
they gather other ideas of a like description, till at last the man is 
bound in a fellowship from which he cannot extricate himself. This 
we believe to be the main source of our erroneous judgments and 
invalid reasonings. They spring not so much from the understand- 
ing as from the prepossessions of the heart, calling up only one kind 
of ideas, and tempting us to look at them exclusively and carelessly, 
keeping us from distinguishing between the things that differ, lead- 
ing us to trace effects to wrong causes, and deceiving us by fail 
appearances and specious analogies. 

82. Fallacies from the days of Aristotle have been 
logically divided into those In Dictione and those Extra 
Dictionem, or, to use a better mode of expression, into 
those in Form and those in Matter. The former are 
found in the very form or expression, and we need look 
no farther ; the latter can be detected only when we look 
to the matter or objects of thought. Whately introduced 
a third division, intermediate between the two others, 
what he calls semi-logical, lying partly in the form, and 
partly in the matter. The division is a very convenient 
one, but cannot be consistently carried out. For Logic 
cannot look at mere material errors ; if it did it would 
have to look at all errors, and therefore at all knowledge, 
historical, ethical, theological, scientific, practical. When 
confined to its proper province, it can look at mistakes 
only so far as they imply violations of the laws of thought. 
But then in order to detect them, it is often necessary to 
look at the matter, at least to the extent of understanding 
what is meant by the propositions and the argument. 
Fallacies of the latter kind constitute what are properly 
called Material fallacies, which, however, must always be 
logical, inasmuch as they imply a disregard of the laws of 
thought, but which may be more or less logical according 
as we have to look less or more to the matter, that is, the 
objects. 

S3, FORMAL FALLACIES. These can be detected 



FALLACIES. 173 

from the expression apart from the meaning or the ob- 
jects. They are simply violations of the fundamental 
laws of reasoning, and may best be exposed by an appli- 
cation to them of the rules of the syllogism. 

Undistributed Middle. Some one proves that Mohammed 
was sincere, and thence quietly infers that he was a good 
man. The reasoning is : 

All good men are sincere ; 
Mohammed was sincere ; 
.•. Mohammed was a good man. 

This violates the general rule that the middle must be 
distributed at least once in the premisses, which is not 
done here, as both premisses are affirmative with the mid- 
dle term in their predicates undistributed. It also vio 
lates the special rule of the second figure, which requires 
one of the premisses to be negative. To legitimate the 
conclusion, the reasoning must take a form in which it 
will be at once seen that the major premiss is not true : 

All sincere men are good men ; 
Mohammed was sincere ; 
.*. Mohammed was a good man. 

Some one shows that religious professors have been 
hypocrites, and thence argues that this man who is a re- 
ligious professor is a hypocrite. This conclusion is valid 
only when he has distributed his middle by showing that 
all, and not merely some, religious professors have been 
hypocrites. 

84. Illicit Process of Major or Minor Term. Thus some 
one allows that all studies are useful which tend to pre- 
pare a man for the practical and professional duties of 
life, but shows that the study of Latin and Greek does 
cot accomplish this end, and thence argues that it is use- 
less. Put the reasoning in proper form, and it is at onco 
seen that there is an Illicit Process of the Major, which ia 
distributed in the conclusion and not in the premiss. 



174 REASONING. 

The studies which prepare for professional life are useful ; 
The study of Latin and Greek does not prepare for such ; 
• It is not useful. 
Whatever represses the liberties of mankind is to be resisted ; 
Among the things which do so are governments , 
.'. Governments are to be resisted. 

Here is an illicit process of the Minor. All that we can 
argue is that some governments are to be resisted. 

83. Negative Premisses. Some one is arguing against 
a doctrine he dislikes, and lays down a number of neg- 
ative positions in the way of objection, and imagines that 
he has established a positive truth. Thus he shows that 
Christianity cannot be proven to be true by its success — 
for Mohammedanism succeeded ; nor by its alleged mira- 
cles — for false religions have had alleged miracles. But 
he is not entitled thereby to draw any positive conclusion, 
certainly not to conclude that Christianity cannot be 
proven by evidence. 

80- Arguments with more than Three Terms. Thus 
when it is argued, " Every one desires happiness ; virtue 
gives happiness; therefore every one desires virtue," we 
have no fewer than five terms : " every one," " desirous 
of happiness," " virtue," " gives happiness," " desirous of 
virtue." It might be possible, no doubt, to express the 
thought so as to exhibit only three terms ; but then the 
fallaciousness of the whole would be evident. When it 
is argued that " as idolatry is a sin ; and as magistrates 
should punish sin ; so they should punish idolatry," the 
fallacy may be concealed by not seeing that there are 
more than three terms, and will at once become visible 
when the comparison is distinctly stated: 

Sin (some sin) should be punished by magistrates ; 
Idolatry is a sin. 

We can draw no conclusion as the middle is not dis- 
tributed. 



FALLACIES. 175 

S7» Fallacies of Conditionals, in denying the antecedent 
and thence denying the consequent, or affirming the con- 
sequent and thence affirming the antecedent. " Prayer 
may be regarded as useful, if indeed we can regard 
our prayers as announcing to Deity what he does not 
know, or changing his eternal purposes ; but as we can- 
not tell the Omniscient what he does not already know, or 
change his plans, we may regard prayer as useless." 
Here we deny the antecedent and can draw no conclusion 
—as prayer may be useful on other grounds. " If this 
man has been much injured, he is unfit to travel ; but he 
is unfit to travel ; so he has been much injured." Here 
we affirm the consequent, but can thence draw no con- 
clusion as to the antecedent, as the man may have been 
unfit to travel from other causes. 

Fallacies in Disjunctives arise chiefly from the dividing 1 ' 
members not making up the whole. But in order to dis- 
cover this, we must look at the objects ; and so this class 
of fallacies falls under the head of Material. 

88. MA TERIA L FALL A GIFS. All fallacies must im- 
ply a violation of the laws of thought in order to bring 
them within the domain of Formal Logic ; but in those 
now to be considered we have to look to the matter in 
order to discover this. 

Ambiguous Teems, specially Ambiguous Middle, in which 
a term is used in different senses in the premiss and 
conclusion, or in the middle as it appears in the two 
premisses. This is the Material Fallacy which approaches 
nearest the Formal Fallacies. In fact it falls under the 
head of Fallacies involving more than three terms. It 
is called semi-logical by Whately. It is logical in that 
it violates the law of thought which requires that there 
be only three notions compared in the three proposi- 
tions. But so far as the language is concerned, there 
seem to be onlv three notions, and we have to look 



176 REASONING. 

beyond the expression to find that under the same phrase 
two notions have been introduced. 

80. In Part First we have dwelt at considerable 
length on the incidental disadvantages of language, and 
specially on those which spring from the ambiguity of 
terms. No evil would arise from the double meaning of 
a word provided we always had a clear apprehension of 
the two senses, and never slid from the one signification 
to the other in the course of the argument. When Paul 
concludes (Rom. iii. 28), that " a man is justified by faith 
without the deeds of the law,'"' he is using the word 'jus- 
tify' consistently throughout, as meaning 'treated by 
jod as free from guilt.' When James says (ii. 24), " Ye 
see then how that by works a" man is justified, and not by 
faith only," he too is using the phrase consistently, 
meaning ' seen to be just before God,' which, he says, 
requires the evidence of works. All candid minds will 
see and acknowledge that in such a case the two state- 
ments are not contradictory, and that both arguments 
may be conclusive. Were we steadily to bear in mind 
that some, as Locke and Kant, understand ' reason ' as 
including ' reasoning,' and that others employ it to signify 
intuitive reason, which excludes ' reasoning,' no mischief 
could arise from the word having two meanings. The 
evil arises from the circumstance that people, both those 
who employ the argument and those te> whom it is ad- 
dressed, are apt to pass from the one sense to the other 
without being aware of it. 

00. Paul says (Col. ii. 16), "Let no man judge you 
in meat, or in drink, or in respect of an holyday, or of the 
new moon, or of the Sabbath-days," meaning by Sabbath- 
day, the seventh day of the week kept at that time by 
many Jewish Christians. But from this some have ar- 
gued that Christians are not now bound to keep the Sab- 
bath-day, meaning the Lord's day, or first day of the 



FALLACIES. 177 

week. Certain of the ancient philosophic sects of Greece, 
as the Stoics, laid down the general maxim, whatever is 
conformable to nature is virtuous and should be attended 
to. The Stoics approved of the principle, understanding 
by nature what is godlike within and without us. Bishop 
Butler says it can be justified only when we properly un- 
derstand our nature, and give to the moral power the 
highest and an authoritative commanding place. But 
some have understood by it, all that is in our nature ; and 
that therefore addictedness to pleasure in youth and to 
gain in old age are allowable, as being agreeable to na- 
ture. Many have argued in former ages that, as a coun- 
try is prosperous according to its wealth (which is true 
in the political-economy use of the phrase), and as a cer- 
tain nation has much wealth (meaning coin or precious 
metals), it must therefore be in a prosperous condition. 
There has been a great deal of logomachy in the dispute 
as to whether there is a reality in heat, light, and color : 
some meaning by these phrases the sensation in our 
frame ; others, the external qualities exciting the sensa- 
tion. Many are puzzled in the present day when they 
hear heat described as a mode of motion, understanding 
by heat the feeling in our organism which, they say truly, 
cannot be a mode of motion, whatever the exciting 
cause may be. There is an ambiguity in the phrases 
' obliged,' ' necessitated,' which has led to false conclu- 
sions being drawn ; some understanding by the phrases 
an external physical compulsion, and others, a moral in- 
clination in the will. Thus some argue that since no man 
has any discredit in what he is necessitated to do, and as 
certain men are necessitated by their nature to do base 
deeds, so they are not to be blamed nor punished. An 
unsatisfactory ethical discussion has been encouraged by 
the uncertain meaning of the word ' good,' which some- 
times means 'morally good,' and sometimes is so widened 
12 



178 REASONING. 

as to include happiness. There are writers who deceive 
themselves as they pass from one of the meanings to the 
other. They show that happiness is a good thing and 
to be promoted, and then go on to speak of it as moral 
good. The words ' conceivable ' and ' inconceivable ' have 
helped much to confuse the controversy between the a 
priori and a posteriori philosophies. Descartes maintained 
that whatever is clearly and distinctly conceived, is to be 
at once believed ; and many have argued that what is 
inconceivable is to be rejected. It is shown in opposition 
to them, that we can clearly and distinctly conceive, in 
the sense of picture or image, many things, such as ghostSj 
in the existence of which we have no faith ; and that 
there are things, such as antipodes, which were reckoned 
inconceivable in one age, and believed in a later age. If the 
defenders of intuitive truth would not render themselves 
the easy prey of their opponents, they should abandon all 
such vague language, and show that there are truths 
which man perceives at once. There is a like ambiguity 
in the statement that all man's ideas are got by expe- 
rience : it is true in the sense that experience is neces- 
sary in order to the ideas springing up ; but it is not true 
that experience apart from an intuitive capacity, can give 
us such ideas as those of moral good and infinity. 

91, Fallacia Accidentis, with its converse, Fallacia a 
dicto secundum quid ad dictum simpliciter. In both, a 
term is used in one of the propositions of the syllogism 
to signify a thing in itself, or in its substance, and in the 
other with certain adjuncts or accidents : as in the hack- 
nied example, " What is bought in the market is eaten ; 
raw meat is bought in the market ; therefore it is eaten.'"' 
It is thus that orators and devotees deceive others and 
are deceived themselves, while they use the phrases loy- 
alty, authority, liberty, faith, religion. These are noble 
qualities in themselves, but men confound the accompaui- 



FALLACIES. 179 

inents with the essence : and they comraend loyalty to a 
person which is disloyalty to a nation ; and obedience to 
a power which has no rightful authority ; and a liberty 
which is licentiousness as being without law ; and a faith 
which is credulity ; and a religion which is superstition. 
It was thus that the cavaliers denounced the covenanters 
and puritans as disloyal, though no set of men ever so 
meant to be loyal. It is thus that some denounce as in- 
fidels all who will not understand as they do the first 
chapter of Genesis, or account as they do for the for- 
mation of the strata of the earth's surface, or the origin 
of animal species. 

92* Equivocation, embracing in it Amphiboly. A mem- 
ber of the House of Commons was supposed to have called 
another member a liar, and a confused dispute arose 
whether that member had been called a liar, or had told 
a lie, when the gentleman charged rose and said sol- 
emnly, " It is quite true and I am sorry for it," meaning, 
" It is quite true he is a liar ; " but understood, " it is 
quite true I said it." To this head may be referred the 
response of the oracle, " Aio te, Aeacida, Romanos 
vincere posse," and the prophecy "The Duke yet lives 
that Henry shall depose." But there are far worse in- 
stances of equivocation than these, in common use. A 
person is charged with having struck another with a stick 
to the danger of his life, and he replies that he did not 
injure him with a stick, though he is conscious all the 
while that he did so with a bar of iron. Or' some one is 
charged with having done a base act on a certain day in 
the forenoon, and he denies it, because he did it after 
twelve o'clock. It is a weapon which has been employed 
in all ages in politics, in courtship, in commercial trans- 
actions : language is employed which is capable of being 
understood in a just sense, but which is meant to leave 
a different impression on those to whom it is addressed. 



180 REASONING. 

The person who resorts to these mean tricks may imagine 
that he is free from the sin of lying ; but the fact is, his 
lying is of a peculiarly aggravated character, as with the 
falsehood there is low and deceitful cunning. Closely 
allied is the fallacy of what is called 

OS. Oblique Expression. It is used by the courtier and 
the flatterer, who keep within the limits of truth in their 
statement, but intend that their words should suggest 
much more to those whom they address. It is employed 
by the calumniator when he does not bring a direct 
accusation — which might be met ; but he hints and in- 
sinuates certain dark charges fitted to raise our worst 
suspicions. We see it exhibited by the guilty man when 
he puts on a look of injured innocence ; or affects a vir- 
tuous indignation because such an offence could be 
charged against him. There are certain speakers guilty 
of it in every sentence, and certain writers exhibit it in 
every page, for they can say nothing clearly and plainly. 
It has been said of Hume, as a historian, that, " without 
asserting much more than can be proven, he gives prom- 
inence to all the circumstances which support his case, or 
glides lightly over those which are unfavorable to it." 

94. FALLACIES OF CONFUSION. Almost all 
paralogisms might be put under the head of Confusion of 
Thought. It is the office of Logic to correct error by ex- 
hibiting the various kinds of confusion into which the 
mind may fall in apprehending, judging, and reasoning. 
The phrase, Fallacy of Confusion, might be restricted to 
those errors which arise from confounding in our minds 
the nature of the notions and the relation of the notions. 
Thus we may be employing in argument a notion of 
which we have a very obscure apprehension. It is a con- 
cept, and we do not know what are the common qualities 
which join the objects in the concept, and in the process 
we suppose these qualities now to be one thing and no^v 



FALLACIES. 181 

another. We are reasoning about the 'good,' and now 
we suppose it to be the morally good and now to be hap- 
piness. Or we use abstract and general terms as if they 
were singulars, and after making jjroper enough predi- 
cations of them, we reach a conclusion in which they are 
to be understood as individual existing things. Plato is 
right in saying that there are ideas in and before the 
Divine Mind ; that these Ideas exist as model forms or 
laws in nature ; and that the human mind may rise to 
the contemplation of them. But he is wrong when he 
speaks of them as existences, like God, the world, and 
the human mind. Scientific men are right when they 
say that the planets are held in their spheres by gravita- 
tion, but they err when they give gravitation a being and 
a power different from the bodies themselves of which 
gravitation is a property. Under this head we may place 
the fallacy of husteron proteron, of placing that which is 
first last, and last first. The good woman mentioned in 
the " Guesses after Truth," had a truth in her mind, but 
expressed it very confusedly, when she thanked God that 
he had placed the Sabbath at the beginning of the week 
instead of the middle of it, as thereby everything was 
kept in order. 

95. Fallacy of Division and Composition, in which a 
term is used in one judgment collectively, and in another 
distributively. In Division, a term is used collectively in 
the major premiss and distributively in the minor, and 
in Composition, the reverse. The liability to fall into 
this fallacy is much furthered by the ambiguity of the 
word "all," which may signify the whole collectively, ot 
may mean every one ; and we fall into a fallacy when we 
use it in one proposition of the syllogism in one sense, 
and in another proposition in the other. It is thus that 
when an army gains a victory, every regiment and soldiei 



182 REASONING. 

in it is apt to claim a share of the credit, though he 
may in no way have helped to produce the result. 
Many a one reasons thus : 

What is no uncommon occurrence may reasonably be expected ; 
To be successful in play is no uncommon occurrence ; 
.•. To be successful in play may be reasonably expected. 

This fallacy is involved in the reasoning of the youth, 
who says or feels : — I may lay oat a certain sum on fine 
clothes and not be in difficulties, and a like sum in jewels 
and not he in debt, and as large a sum in travelling with- 
out spending all my money, and concludes that he may 
procure all these enjoyments. The same error is involved, 
but in an opposite way, when the greedy man being asked 
to subscribe to one charity after another, and finding that 
if he gives to all he will be ruined, determines to give to 
none. " Two distinct objects may, by being dexterously 
presented again and again in cuiick succession to the 
mind of a cursory reader, be so associated together in his 
thoughts as to be conceived capable, when in fact .they 
are not, of being actually combined in practice. The fal- 
lacious belief thus induced, bears a striking resemblance 
to the optical illusion effected by that ingenious and 
philosophic toy called the Thaumatrope, in which two 
objects painted on opposite sides of a card — for instance, 
a man and a horse, a bird and a cage — are, by a quick 
rotatory motion, made to impress the eye in combination 
so as to form one picture, of the man on the horse's back, 
the bird in the cage." ( Whately.) 

96. Imperfect Division. This fallacy specially appears 
in Disjunctive Reasoning, in which it is implied in order 
to the validity of the reasoning, that the members make 
up the whole, and that they exclude one another. But it 
often happens that the parts named do not make up the 
whole : 



FALLACIES. 183 

If it is decreed that you will recover from this disease you do not 
need a physician ; if it is decreed that you will not recover 
you do not need a physician ; 

But you will either recover or not recover ; 
. You do not need a physician. 

Whereas there may be a third supposition ; that it is de- 
creed that you are to recover by means of a physician. 

Quite as frequently the divisions are not exclusive, in 
other words, cross each other. In the famous con- 
troversy between the a priori and a posteriori philoso- 
phies, the supporters of the latter shut their opj)onents 
up into the dilemma, that such ideas as those of power 
and moral good are to be had either from some innate 
power exclusively or from experience, and then show 
that experience has to do with their formation ; but the 
truth may be that the two combine ; the native power 
may work in our experience, and on the occasion of our 
experience.* 

i)7. We now come to consider fallacies arising, not so 
much from the terms, as from their relation to one an- 
other in the reasoning. 

Fallacy of Shifting Ground, as when the advocate or 
opponent of a cause begins as if he were about to prove 
it to be good and right, and as he proceeds shows that 
some good may be derived from it ; or that it is wrong 
and bad, and shows that it has led to certain supposed 
evil results. Under this head may be placed the common 
practice of persons professing to prove that a certain 
deed has been done, but dwelling chiefly on the enormity 
or the excellence of the deed, with the view of rousing 

* Triptolemus Yellowley thought there were two ways of draining Braebaster 
Loch, one down the Linklater Glen, the other by the Scahnester burn. But the 
Udaller saw the imperfection of his division. " There is a third way ; let each 
of us start an equal proportion of brandy, lime juice, and sugar, into the loch, 
and let us assemble all the jolly TJdallers of the country, and in twcnty-foni 
hours you shall see dry ground where the loch of Braebaster now is." 



184 BEA80MJS/U. 

the feelings and to prevent it being seen that they have not 
established their point. Francis Bacon is charged with 
having received an estate from his Mend the Earl of Essex, 
and afterwards being unkind to him ; and the strength of 
the writer is expended in dwelling on the evil of ingrati- 
tude, especially on the part of so great a man, instead of 
proving the alleged facts. In oral controversy how often 
is it found that you combat "both your opponent's pre- 
misses alternately, and shift the attack from the one to the 
other, without waiting to have either of them decided 
before you quit it. ' And besides ' is an expression one 
may often hear from a disputant who is proceeding to a 
fresh argument, when he cannot establish, and yet will 
not abandon, his first." Under this head may be placed : 

98. Fallacia Plurium Interrogalionum consists in ask- 
ing two or more questions as if they were one and the 
same, and when one of them is answered it is interpreted 
as applied to the other. It is a trick of a low kind often 
resorted to by lawyers in examining witnesses, with the 
view of puzzling tliem, and turning their answers to a 
wrong account. " You were swayed by the love of money 
in the transaction?" (meaning exclusively,) to which the 
witness answers " yes," (meaning in part.) Another ques- 
tion follows : "Iu being swayed by money you were 
acting selfishly in the transaction ? " The fallacy appears 
in higher matters. Thus the utilitarian puts to us the 
questions : " You deny that virtue consists in utility ? " 
" Yes." " Then you deny that utility is a good thing." 
The faUacy is to be met by accurately answering each 
question separately. 

99. PETIT10 PRINGIPII, or BEGGING OF THE 
QUESTION, "in which one of the premisses either is 
manifestly the same in sense with the conclusion, or is 
actually proved from it." A man may prove that the 
Bible comes from God because it contains certain ele- 



FALLACIES. 185 

vated doctrines which could not be discovered by the 
natural sagacity of the writers ; but after he has done 
this he cannot turn round and prove that these doctrines 
are true because they are contained in the Bible. We 
ought not to prove the existence and unity of God from 
its being contained in Scripture, and then prove the truth 
of Scripture from its giving us such high views of the ex- 
istence, unity, and nature of God. 

100. And here it may be proper to remark that the Syllogism or 
Syllogistic reasoning is not, as has often been alleged, a Petitic 
Principii. As put in syllogistic form, the premiss does not in any 
sense depend on the conclusion; and the conclusion follows, not 
from one of the premisses, but from the two, or rather from the re- 
lations between the things compared in the premisses. It is when 
the relations predicated in the two propositions are brought before 
the mind that it sees the force of the inference. 

101. Arguing in a Circle is the common manifestation 
of the Petitio Principii. The person covertly, it may be 
ignorantly, assumes a fact or principle, and by means of 
it reaches a conclusion, which he is found after a while to 
be employing to establish the fact or principle with which 
he set out. Thus we find persons arguing that their church 
is the true one because sanctioned by God ; and that since 
it is the true church, God has sanctioned it. Or they reach 
the truth of the Bible from the authority of the Church, 
and infer the authority of the Church from the Bible. A 
man maintains that his party is good because it promotes 
good measures ; and that a measure is good because pro- 
moted by his party. Malebranche is believed by many 
to have become involved in this circle, when he proved 
the existence of an external world by the authority of 
Scriptare ; and he certainly did so, if it be impossible to 
establish the authority of Scripture unless you assume 
the existence of an external world. Much of the elabo- 
rate reasoning employed in the discussion of intricate 
subjects — for example, that of Spinoza in his Ethics — is a 



186 REASONING. 

movement in a circle — like that of a man who, after toiling 
for hours in the dark, comes to the place from which he 
started. It is evident that the more involved the chain, the 
more difficult to detect the unsatisfactory junctions. The 
most effective way of exposing the whole, is to insist on 
narrowing the circle, and so spreading out the links that 
we may see the feeble place, where the conclusion is em- 
ployed to support the premiss, and the whole chain made 
to hang on nothing. 

102. IGNORATIO ELENGHI, or IRRELEVANT 
CONCLUSION. Logicians suppose that in discussion 
the opponent should prove the elenchus or contradictory 
of your doctrine ; and when he fails to do this, and es- 
tablishes a different proposition, he is said to be guilty of 
an Ignoratio Elenchi. But the language may be so 
widened as to include under it all cases of Irrelevant 
Conclusion — that is, in which persons establish, not the 
conclusion which they ought, but another which may be 
mistaken for it. The dispute is, whether any one has a 
right to compel a father to educate his child in a way dif- 
ferent from what he is doing, in religion or in something 
else, and one of the disputants thinks he has settled the 
whole question when he has shown that the father is 
educating his child wrong. Locke in showing that the 
syllogism is of little or no value, proves that man can 
reason without the use of syllogisms. " There are many 
men that reason exceeding clear and rightly, who know 
not how to make a syllogism." " God has not been so 
sparing to men to make them barely two-legged crea- 
tures, and left it to Aristotle to make them rational." 
Macaulay in his Article on Bacon, thinks he has proven 
that a knowledge of the canons of induction is of little 
use, since men, without knowing them, are practising 
them from morning to night. Under this general head 
may be placed several other fallacies. 



FALLACIES. 187 

103. The Fallacy of proving only Part of the Question, 
A.s wlien a man is charged with murder, and the prose- 
cutor proves that he killed a man. The judge and jury 
will insist that it be farther shown that he did the deed, 
not in self-defence, or from provocation at the moment, 
but with malicious intent. A person is denounced as a 
liar, and his accuser when asked for his evidence shows 
that he did make certain misstatements, it may be from 
misapprehension or misinformation. "When the agri- 
culturist objected to the Shetland plough with only one 
handle, Magnus Troil proved part of his point when he 
replied, " Tell me how it were possible for Neil of Lup- 
ness, that lost one arm by his fall from the crag of Nek- 
brekan, to manage a plough with two handles ? " 

104. Fallacy of Objections, that of concluding that a 
proposal is to be set aside because there are objections to 
it — as if the captiousness of men were not prepared to 
object to anything, even to the existence and worship of 
Grod. It is not enough to show that there are objections ; 
it must be shown that there are stronger reasons against 
it, than for it. Thus in one of the rising cpiestions of the 
day, when it is proposed to appoint young men to public 
offices by competitive examination, an opponent thinks it 
sufficient to object that at times you might thus get a 
person who has no great business capacity ; whereas it 
properly devolves on him to show that by this mode of 
appointment you would not get young men of such high 
business talents and character as by the method now 
practised of political patronage. 

103. Argumentum ad Hominem. As all reasoning is 
ex concessis, we are entitled in reasoning with any one to 
proceed on the principles avowed by him, though these 
might not just be the principles to which we might appeal 
in dealing with others or with mankind generally. Our 
Lord often employed this method in dealing with the 



188 REASONING 

cavils of the Pharisees. The argument, however, will not 
be acknowledged as valid by those who do not admit the 
principles on which it proceeds. That loose appeal made 
to faith in the last age by so many German and British 
writers, is not allowed to be legitimate by those who in- 
sist on your proving by the proper tests that a faith must 
be intuitive, or that it is supported by sufficient mediate 
evidence, before they are inclined to yield to it. It is not 
an honest use of the argumentum ad hominem, when we 
take advantage of premisses which those with whom we 
are arguing allow, but which we do not ourselves believe, 
— except, indeed, when our aim is simply to make them 
doubt of their premisses by showing the consequences to 
which they lead. 

106. Argumentum ad Populum, or an appeal to prin- 
ciples cherished by the great body of the people. It is 
allowable only when the principles are right and proper 
in themselves, and are conscientiously entertained by 
those who advocate them. It is not legitimate when 
they are wrong in themselves, or when he who urges 
them is doing so hypocritically. It will commonly hap- 
pen in the end that such a deceitful use of the argument 
will turn against the person enjoying it. In no case is 
it allowable to employ this argument to stir up a malig- 
nant spirit or violent acts. 

107. Argumentum ad Verecundiam. It consists of an 
appeal to antiquity, to the opinions of ancestors, to the 
religion of the country. This line of argument may prove 
that we are not rashly to disturb the established order of 
things ; but it goes no farther. It does not tend to prove, 
that if we are constrained otherwise by truth or by duty, 
we must believe as our forefathers did, or decline to dis- 
turb the present order of things. 

108. Argumentum ad Ignorantiam, as when you insist 
on a man believing a thing because he knows nothing to 



FALLACIES. 189 

the contrary. It is thus that people have been frightened 
by horrid pictures, drawn by priests or pretenders, of the 
world to come. It is thus that some would have us be- 
lieve in animal magnetism, in clairvoyance, and the like, 
because they exhibit phenomena which we cannot explain. 
The legitimate conclusion in such cases is, that we should 
suspend our judgment, and wait for light to come from 
true religion, or scientific research. 

109 '. Fallacy of Pretension. We are inclined to intro- 
duce some such head as this, to include certain very 
common cases of wrong inference. It would embrace, for 
instance, the Fallacy of References, in which there is an 
appeal by authors or speakers to passages or to authorities 
which are not expected to be very narrowly searched, or 
which, if narrowly scrutinized, do not bear out the con- 
clusion. It is thus that Buckle, in his work on Civili- 
zation, has deceived (we do not say intentionally) many 
by numerous quotations which, if narrowly sifted in their 
historical connection, are not fitted to bear up all that he 
would rear on them. It is thus that a dogmatic air over- 
awes many who are not inclined to think for themselves 
or institute an independent inquiry. Many feel as if such 
men as Hobbes and Comte must be speaking truly and 
with a profound knowledge of their subject, when they 
utter their statements so clearly and so confidently — where- 
as all this may have arisen fi'om their never having looked 
at anything more than one side of a very complex ques- 
tion. Under this head we place the Idola TJieatri of 
Bacon, or the deceiving influence exercised by great 
doctors, heads of sects, and leaders of opinion. 

110. Argument from Consequences. This is allowable 
in questions of pure expediency, as, for example, in con- 
sidering a proposal to pass a law for the suppression of 
intemperance, or gambling, or licentiousness ; we ought 
to inquire whether it would effect the end in view. But 



190 REASONING. 

when the question is one of truth or right, we should not 
in the first instance appeal to results. There is a con- 
stant tendency on the part of some, when a new scientific 
truth is divulged, to reject it because it may produce evil 
consequences by undermining religious beliefs, or good 
social sentiments. But if a doctrine be true, and a deed 
be right, the consequences must be good whether we see 
it or not. After we have established the truth or false- 
hood of a doctrine on independent evidence, then we may 
allowably trace the consequences — always, however, in a 
spirit of candor and fairness. 

Ill, Mistakes as to the Onus Probandi. When any one 
makes a positive affirmation, the Burden of Proof un- 
doubtedly lies on him, and his evidence should be such 
as can stand the laws of evidence in the particular de- 
partment. If it be a mathematical truth, he must dem- 
onstrate it by principles self-evident, necessary, univer- 
sal. If it be a scientific truth, he should bring evidence 
that can stand the tests of the canons of induction. If 
it be a historical event, he must show that it can stand the 
tests of historical criticism. If it be reached by deduc- 
tion, it may be tried by the syllogism. But if he has 
failed to give sufficient proof, he is not entitled to insist 
on those who may not give in to his affirmation, proving 
the contradictory of it. They may very properly content 
themselves with suspending their judgment till proof is 
adduced. For example, if a man says a particular plant 
is to be found in a certain country — say azaleas in Scot- 
land — we expect him to produce the plant. But he is not 
entitled to demand of us that we go round the whole 
country and show that there is no such plant. It is often 
easy to disprove a general statement by an individual 
case. If a man were to say that all the blessings which 
God sends are universal or common to the whole race, 
you could confute him by showing (in the third figure of 



FALLACIES. lyl 

the syllogism) that certain blessings, such as the means of 
education, had not been placed within the power of all 
mankind. But to prove a general negative is often dim- 
cult or impossible ; for you would have to go round all 
possible cases, and show that no one of them admits of a 
positive affirmation being made regarding it. 

112. We now come to consider certain Fallacies 
usually treated of in works of Formal Logic, but conduct- 
ing us into Particular or Objective Logic, which looks at 
thought as directed to special classes of objects. No 
doubt there are violations of the laws of discursive 
thought involved, but in order to find out what they are, 
and how they are to be remedied, we must go to other 
departments of knowledge. 

Fallacies of Analogy. By analogy we are to understand, 
not the resemblance of one thing to another, but the re- 
semblance of ratios or relations. Thus the sovereign of a 
country is said, by analogy, to be the head of the country, 
because he bears the same relation to the country as the 
head does to the body. Two fallacies may spring from 
the use or abuse of analogies. First we may suppose 
that the things related resemble each other because their 
relations do. The wing of a bird and the wing of a but- 
terfly are said by naturalists to be analogous, for they 
serve the same purpose, that of flight ; but the two 
members do not resemble each other in their structure. 
We are exhorted by our Lord in praying to God, to imi- 
tate the importunity of the woman who continued to 
apply to the judge till she gained her case ; but we are 
not to understand that Grod resembles that judge in 
character, or the motives by which he is swayed. An- 
other fallacy arises from carrying the analogy too far. 
Thus some have argued that since all nations resemble ani- 
mals, in having a period of childhood, youth, and maturity, 
they will therefore resemble them in having a time of de- 



192 REASONING. 

creptitude and death — whereas there may be causes al 
work in certain nations, such as education and Christian- 
ity, which will save them from the latter stages. The 
argument from Analogy is : " Things resemble each other 
in certain known respects ; they will therefore resemble 
each in certain other and unknown respects." This is an 
argument which is often conclusive. Thus the connois- 
seur argues : this painting resembles the paintings of 
Rubens in certain characteristic marks, and must resem- 
ble them in this respect also, that it has been produced 
by the same hand. Thus it is that the anatomist finding 
one fossil hind leg of an animal, concludes that the other 
must have been like it. It is in a great measure by this 
principle that the palaeontologist can construct the whole 
animal from a few bones found in the dust of the earth. 
It is the province of Inductive Logic to lay down some 
rule to guide us as to when the conclusion is valid, and 
when it is invalid. Formal Logic can assist us no way at 
this place. All that it can do is to show where error may 
lurk, and insist on our seeking to obtain some general 
principle (as a major) to guide and guard us. 

113, Imperfect Enumeration. In all departments of 
science and practical knowledge, general laws are gained 
by the observation of particular facts. But what number 
and what kind of observations are sufficient to entitle us to 
declare that we have discovered the law V A sailor reasons : 
' Three times did I set sail on a Friday, and in each of 
the voyages I encountered a storm ; it is clear that Fri- 
day is an unlucky day.' Another met once or twice with 
a calamity after sitting at a table where there was a com- 
pany numbering thirteen, and resolves always to leave a 
company when he discovers it to be composed of this 
number. A third met with calamities on several occa- 
sions when he persevered in a journey after a hare had 
crossed his path, and he now turns back whenever that 



FALLACIES. 193 

animal crosses the road on which he is travelling. Every 
enlightened man sees that these are cases of narrow enu- 
meration. But what is a sufficient enumeration ? It can 
easily be shown that the sufficiency does not depend on 
the number of the cases. Mr. Mill puts the question : 
" Why is a single instance in some cases sufficient for a 
complete induction, while in others myriads of concur- 
ring instances, without a single exception known or pre- 
sumed, go such a very little way towards establishing a 
universal proposition?" and declares that he who will 
answer this question is wiser than the ancients. Bacon, 
followed by Sir J. Herschell, Mr. Mill, and others, have 
tried to answer it by means of Prerogative Instances 
( § 71) and Canons of Induction, and have been so far 
successful. The Logic of Induction is seeking to lay 
down principles which may decide for us when we have 
such an enumeration as to authorize us to say that we 
have reached a law. But Formal Logic can do nothing 
more than warn us against trusting in imperfect enumer- 
ations, and require us to look out for some principle to 
authorize the conclusion we would draw. 

111. Non Causa pro Causa. The inquiry into Causes 
is not the same as the inquiry into Laws, referred to in 
last section. In the inquiry into Laws, we are seeking a 
mere co-ordination of facts ; in the inquiry into Causes we 
are seeking after antecedent agents having a producing 
power. The one inquiry, as well as the other, carries us 
beyond Formal Logic into Inductive Logic, and indeed 
into the Natural Sciences which treat of objects. Formal 
Logic, however, can guard us against certain errors, and 
draw our attention to some important distinctions. 

115. Post Hoc ergo propter Hoc. A remarkable meteor 

was seen in the sky, and followed by a dreadful national 

calamity : a conjunction among the planets was followed 

by a royal marriage which issued in far-reaching conse- 

13 



194 REASONING. 

quences; and the superstitious conclude that one oi 
the facts had some kind of causal connection with the 
other. "We have outlived these weaknesses of past ages : 
but we have not outgrown the fallacies on which they 
proceeded. A country or college has prospered under a 
certain government or management, and some conclude 
that it was because of the government or management, 
and oppose all projected improvements. 

116. Fallacy of mistaking Sign for Cause. The quack 
doctor falls into this, when on seeing certain spots on the 
body he attacks and removes them, thereby, it may be, 
sending the malady farther into the frame, instead of 
curing it in its seat. The quack statesman is guilty of the 
same error, when discovering the existence of ignorance 
and crime in a country he contents himself with punish- 
ing them, instead of trying to remove the deep moral 
causes from which they spring. Buckle has, as it ap- 
pears to us, fallen into the fallacy ; he traces all civiliza- 
tion to mere intellectual power, excluding moral causes : 
whereas the intellect in many cases, as in Scotland and 
the United States, was awakened by moral causes of 
which the intellectual life was, properly speaking, the 
effect. 

117* In order to keep us from falling under the power 
of these fallacies, Logic calls our attention to two im- 
portant distinctions. There is the distinction between 
the Causa Essendi and the Causa Cognoscendi. The for- 
mer is the objective cause in the powers of nature or of 
God ; the latter, the facts or means by which we come to 
know the objective cause of the occurrence. The two are 
often confounded by much the same language being em- 
ployed by us to denote them. Thus we speak of the 
ground being wet because it has rained ; and of its hav- 
ing been rain because the ground is wet. It is evident 
that the Causa Cognoscendi is often an effect indicating 



FUNDAMENTAL LAWS OF THOUGHT. 195 

the Causa Essendi; thus the melting of snow may be a 
proof or a sign of the rise of temperature which has made 
the snow to melt. Of very much the same character is 
the distinction between Reason and Cause ; the Reason 
being that which brings conviction to us, and the Cause 
that which produces the phenomenon. The increase of 
temperature is the cause of the melting of the snow, but 
the melting of the snow as being an effect may, on being 
contemplated by us, be the means of revealing the action 
of the Cause. 



FUNDAMENTAL LAWS OF DISOUKSIVE THOUQHT. 

118. It now only remains to try to enunciate the 
fundamental laws which lie at the basis of all Logical op- 
erations. These work in our minds without our being 
conscious of them — we are as little conscious of them, as 
we are of the physiological laws involved in our breathing. 
We can discover them only by careful observation and 
analytic generalization of the operations of discursive 
thought. A knowledge of them does not assist us in 
spontaneous reasoning, but it is of great value to all who 
would reflectively acquaint themselves with the processes 
of thinking. They are such as the following : 

110. I. The Law of Identity, which may be expressed, 
"the same is the same, perceived it may be at different 
times and with different concomitants." This rules all 
cases in which we draw an affirmative proposition from a 
proposition or propositions, in which the relation of the 
two terms is one of identity. Thus it being given that 
" Jonathan Edwards is the greatest American metaphy- 
sician," we get the Implied Judgment " the greatest 
American metaphysician was Jonathan Edwards ; " or, it 
being farther allowed that " Jonathan Edwards was the 



196 G0NGLU8I0N. 

Missionary to the Indians at Stockbridge,' we get bj 
reasoning the Conclusion that " the Missionary to the 
Indians at Stockbridge, was the greatest A meriean meta- 
physician." 

120. II. The Law of Contradiction. This law is " it 
is impossible for the same thing to be and not to be at the 
same time." Or bringing out a farther aspect of the same 
truth, it may take the form : " A thing cannot have, and 
not have, the same attribute at the same time." It rules 
in all cases in which we get a negative proposition from a 
negative proposition by implication, or from negative 
propositions by reasoning, as when it is given us that, 
" Francis Bacon is not the same as Boger Bacon," we say 
that " Koger Bacon was not the same as Francis Bacon," 
or, with another proposition allowed, that " Francis Ba- 
con was the expounder of the Inductive Method," so 
" Roger Bacon was not the expounder of the Inductive 
Method." 

121. III. The Law of Excluded Middle, Lex Exclusi 
Tertii aut Medii ; that is, either a given judgment is true, 
or its contradictory — there is no middle course or third 
supposition. Thus it must either be true or not true 
that " God exists ; " and it must either be true or false 
that " this man was ignorant of the deed ; " and if it 
can be shown that he was not ignorant of it, you cannot 
look upon him as if he was ignorant. 

122. TV. The Principle of Equality, " things which 
are equal to the same things, are equal to one another." 
It is thus we argue that 2 + 2 = 4; and 2 x 2 = 4; 
therefore 2 + 2 = 2x2. 

In all cases in which the propositions are Equivalent 
(P. II., § 14), these are the sole regulating principles. 
But where the propositions imply Extension and Compre- 
hension, other Laws come in and act along with these. 

123. V. The Dictum of Aristotle, " whatever is predi- 



FUNDAMENTAL LAWS OF THOUGHT, 197 

cated of a Class Notion, may be predicated of all that ia 
contained in it." This is seen to be true on, the bare con- 
templation of the nature, of the extension, of a concept. 
Combine this principle with that of Identity, and we get 
Affirmative Judgments implied or inferred. Thus as " all 
plants die," so " some plants die," and as " Coniferae are 
plants," so " Coniferee die." Combine this principle with 
that of Contradiction, and we draw negative propositions. 
As " no men are perfect," so " some men are not perfect," 
and " the Greeks " " who were some men," " were not 
perfect." These principles, the Dictum combined with 
the Law of Identity in affirmatives, and of Contradiction 
in negatives, rule all ordinary syllogistic and conditional 
reasoning. 

Combine the Dictum with the principle of Excluded 
Middle, and we get a number of Implied Judgments. 
Thus we argue that if it be false that " no metal is heavier 
than water," it must be true that " some metals are heavier 
than water." Eeductio per Impossibile (P. III., § 40), pro- - 
ceeds on these two principles. 

124:. VI. The Principles of Attribution, " every at- 
tribute implies a thing of which it is an attribute." Or, 
it may take a subordinate form, " All that is in an attribute 
is in the thing that contains the attribute," or, as Leib- 
nitz expresses it, " Nota notse est nota rei ipsius." This 
law has a place in Abstraction (P. I., § 11) ; in Imme- 
diate Inferences from Privative Conceptions (P. IT., § 49), 
and in all reasoning in Comprehension (P. III., § 42), that 
is, reasoning in which we specially look at the attributes. 
Thus we argue that as intelligence, conscience, and free 
will, make the beings who possess them moral and re- 
sponsible agents, so man, as possessing these, must be 
regarded as a moral and responsible agent. 

125. VII. The Law of Division, " the dividing mem- 
bers make up the whole class." This is the principle — al- 



198 CONCLUSION. 

ways along with the Dictum — regulating Disjunctive Rea- 
soning, as when we argue that if a man has not taken 
two of three possible roads, he must have taken the third. 
Combined with the principle of Excluded Middle, it regu- 
lates reasoning in which we argue on the supposition 
that the members exclude one another. " If this man 
must be either a fool or a knave," it follows if he is not a 
fool, " he must be a knave." 

12(>. VDII. The Principles of Whole and Parts. 
" What is true of the whole is true of each of the parts." 
This holds good of parts whether they be sub- classes or 
attributes. This principle helps to guide us in Subalter- 
nation, and in all reasoning involving Extension and Com- 
prehension. Another Principle to be placed under the 
same head is, " The parts make up the whole ; '' a prin- 
ciple involved in all reasoning which proceeds on the 
completeness of Division. 

127- I" looking at the discursive operations of the mind, we 
have constantly come to such principles as these. The consider- 
ation, however, belongs not to Logic, but to Metaphysics (P. I., § 1), 
or the science of First or Fundamental truths. The author of this 
treatise has treated of them, of their nature and mode of develop- 
ment, in First and Fundamental Truths. He has there shown that 
such principles are Intuitive, that is, are seen to be true at once ; 
and this not by any form in the mind, but by the capacity which the 
mind has to contemplate objects, and by the exercise of that capacity 
in looking at objects. He has shown that the Law is not consciously 
before the mind when it is exercising it, and that it is in looking at an 
individual object, or judgment, that it is called forth. The mind has 
not consciously before it the Law of Equality Avhen it declares that if 
A is equal to B, and B to C, then A must be equal to C. It reaches 
the conclusion at once on the contemplation of the equal lines. The 
Law of Equality is discovered by us by a generalization of the individ- 
ual judgments. 



APPENDIX. 



I.-EXERCISES AS TO FORMS. 
The Notion. 

1. Are the following Singulars, Abstracts, or Universals, ana 
if Universals, are they Generalized Abstracts or Generalized Con ■ 
cretes, viz. : Aristotle, Rationality, Rational, Man, Beauty, Good, 
The Good, Homeless, The Creator, Creature, Resolute, Plant, 
Mammal, Substance, Mind ? 

What sort of terms are the following, viz. : Multitude, Thii 
Regiment, David King of Israel, The First King of Rome, Th* 
greatest living Sculptor, The Dog Cesar, This Dog, That Bird 
Flying, The most distinguished Soldier in the Army, Husband , 
Husband and Wife, 

" The glass of fashion and the mould of form, 
The ohserved of all ohservers." 

2. What are the Terms in the following, and what sort ot 
Terms ? " Thou (FalstafF) didst swear to me upon a parcel gilt 
goblet, setting in my Dolphin Chamber, at the round table, by 
a sea-coal fire, upon Wednesday in Whitsunweek, when the 
prince broke thy head for liking his father to a singing man of 
Windsor ; thou didst swear to me then, as I was washing thy 
wound, to marry me and make me my lady thy wife. Canst 
thou deny it ? Did not good wife Keech, the butcher's wife, 
come and call me Gossip Quickly ? Coming in to borrow a me«9 
of vinegar; telling me she had a good dish of prawns, whereby 
thou didst desire to eat some ; whereby I told thee they were ill 
for a green wound ? And didst thou not, when she was gone 
down stairs, desire me to be no more so familiarity with such 
poor people, saying, that ere long they would call me madam." 



200 APPENDIX. 

" Because A F is equal to A G, and A B to A C, the two sidea 
F A, A C are equal to the two G A, A B, each to each ; and they 
contain the angle FAG common to the two triangles AFC, 
A G B ; therefore the base F C is equal to the base G B, and 
the triangle AFC to the triangle A G B ; and the remain- 
ing angles of the one are equal to the remaining angles of the 
other, each to each, to which the equal sides are opposite, viz. : 
the angle A C F to the angle A B G, and the angle A F C to the 
angle A G B,' 1 &c. 

" To be, or not to be, tbat is the question ; 
Whether 'tis nobler in the mind to suffer 
The stings and arrows of outrageous fortune, 
Or to take arms against a sea of troubles, 
And, by opposing, end them ? To die— to sleep — 
No more : and, by a sleep, to say we end 
The heart-ache and the thousand natural shocks 
That flesh is heir to — 'tis a consummation 
Devoutly to be wished. To die ? to sleep 1 
To sleep— perchance to dream ; aye, there's the rub, 
For in that sleep of death what dreams may come, 
When we have shuffled off this mortal coil, 
Must make us pause." 

S. Are the following pairs of Notions Contrary or Contradictory 
viz. : Sweet and Bitter, Organic and Inorganic, Greek and Bar- 
barian, Wise and Foolish, Animate and Inanimate, Finite and Infi- 
nite, Alive and Dead, Short or Long, Existent and Non-existent ? 

4. What sort of reality is there in the following, viz. : Popu- 
larity, The Rose Tribe of Plants, Gravitation, The Vine, Love of 
Fame, Imagination, Roman Citizen, Heat, Cold, Blue, Substance, 
Body? 

5. Logically Define Notion, Percept, Abstract, Concept, Genus, 
Species, Differentia, Judgment, Equivalent Proposition, Attribu- 
tive Proposition, Conditional Proposition, Disjunctive Proposi- 
tion, Implied Judgments, Conditional Reasoning, Disjunctive 
Reasoning, Reasoning in Comprehension, Sorites, Fallacy, Am- 
biguous Middle, Petitio Principii, Irrelevant Conclusion. 

6*. Logically divide and subdivide Notion, Judgment, Reason- 
ing, Fallacy. 

7- Analyze General Notion, Collective Notion, Judgment, 
Argument, A Horse Galloping, Unappeasable Revenge, Remorse 
of Conscience. 



APPENDIX 201 



Judgment. 

8, Point out Subject and Predicate aud designate the Quality 
and Quantity of following, viz. : 

A soft answer turnetb away wrath. 

The man's heart is not in the right place. - 

Dogs bark. 

Great is the work of life. 

Sailors are needed for the vessel. 

It is wrong to put an innocent man to death. 

It is the duty of every man to fear God and honor the 

king. 
Man is capable of living in a greater variety of climates than 

any of the lower animals. 
There was no possibility of substantiating the allegations. 
The evidence proves that Phalaris was not the author of thn 

Epistles. 
Few patriots have been disinterested. 
All gold mines cannot be wrought with profit. 
The eagle lost much time when he submitted to learn ot thi . 

crow. 
The English can scarcely be said to be humble-minded. 
Nothing is so easy as to object. 
" In jewels and gold men cannot grow old." 
There is no place like home. 
None but the brave deserve the fair. 
None but whites are civilized. 

9. What is the Nature of the Terms in the following '{ Ate 
the Propositions Equivalent or Attributive ? 

The crocodile is a reptile. 

Alexander was a great conqueror. 

Alexander was the greatest conqueror of antiquity. 

Logic is the science of the Laws of Discursive Thought. 

" The most sublime act is to put another before thee." 

3x3 = 9. 

If the clouds rise from the hill-top it will be a fine day. 

If A = BthenC = D. 

The event must have occurred either on Saturday or Sunday 



202 APPENDIX. 

" Man is endowed with the capacity of laughter." Undei 
what head of Predicables would this be put by Aris- 
totle ? By Porphyry ? And in this Treatise ? 

10. Convert the following : 
Every circle is a conic section. 

Two straight lines cannot enclose a space. 

No brutes are responsible. 

Some students are diligent. 

Some students do not fail in anything. 

Perseverance is a condition of success. 

Perseverance is the condition of success. 

Washington was the first American President. 

11. Put the following in the forms of Opposition : 

The Duke of Wellington was the conqueror at Waterloo. 
Dogs bark and bite. 
What are the Contradictories ? 

12. Interpret the following as to Denomination, Extension, 
and Comprehension : 

Man is fallible. 

David was the sweet Psalmist of Israel. 

The man who slanders his neighbor is not innocent." 

13. What Implied Judgments can be derived from " Benevo- 
lent actions are commendable." 

14. Put the following in correct form as a Conditional, anu 
indicate the Terms, the Antecedent, and Consequent : " This 
patient will recover if he takes care of himself." Put it in Cate- 
gorical Form, and indicate the Subject and Predicate. 

Reasonikg. 

15. Examine the following, and say if they are valid ; and if 
so, according to what principle : 

David was the youngest son of Jesse ; 
David was the youth who slew Goliath ; 
.*. The youngest son of Jesse was the youth who slew Goliath. 
Logic is the Science of the Laws of Discursive Thought ; 
Metaphysics is not the Science of the Laws of Discursive 
Thought ; 
*. Logic is not Metaphysics. 



APPENDIX. 203 

10. Put the following in Syllogistic Form. ; indicate the 
Major, Minor, and Middle Terms ; the Major, and Minor 
Premisses, and conclusion; and the Mood and Figure: 

No one is free who is enslaved by his appetites ; a sensual- 
ist is enslaved by his appetites ; therefore a sensualist 
is not free. 
Heavy dews fell last night and so it has not been cloudy. 
From the case of the soul and body we see that there are 
some things to be believed which cannot be compre- 
hended. 
17. Supply the wanting proposition in the following : 
No branch of science has reached perfection ; 
All branches of science deserve to be cultivated. 



All horned animals are ruminant, 
.•. The elk is ruminant. 

The adaptation in the shoulder-joint is effected; 
.•. It must have had a cause. 

18. Put the following in Syllogistic Form, supplying Premis- 
ses when necessary, and indicating Mood and Figure : 

When Columbus was sailing the ocean in search of a new 
world, he fell in with a flock of land birds and con- 
cluded that he could not be far from land. 

It has been argued by some that electricity is the agent by 
which the nerves act upon the muscles. But that this 
is not the case appears from the fact that electricity may 
be transmitted along a nervous trunk when a string i? 
tied lightly round it ; while the passage of ordinary ner- 
vous power is as completely checked by this process as 
if the nerve had been divided. 

His imbecility of character might have been inferred from 
his proneness to favorites ; for all weak princes have 
this failing. 

'•' Suppose ye that these Galilaeans were sinners above all 
the Galilseans because they suffered such things ? " 



204 APPENDIX. 

The Scriptures cannot come from God because they contain 
some things which cannot be comprehended by man. 

That persons may reason without language is proven by 
the circumstance that infants reason and yet have no 
language. 

Bolingbroke, in arguing against the truth of the Christian 
religion, shows that the Christian religion has bred 
contentions. Burke answered him by showing that 
civil government had bred contentions. 
"The barbarians of the isle of Melita, when they saw the 
venomous beast hang on Paul's hand, said among them- 
selves, No doubt this man is a murderer, whom though 
he hath escaped the sea, vengeance sufifereth not to live 
Howbeit, they looked when he should have swollen or 
fallen down dead ; but after they had looked a great 
while and saw no harm in him, they changed their 
mind and said, he is a god." 

The dervis who told the merchants that they had lost a 
camel, blind in his right eye, lame in his left leg, with- 
out a front tooth, loaded with honey on one side and 
wheat on the other, describes the steps which had 
passed through his mind, " I knew that I had crossed 
the track of a camel which had strayed from its owner, 
because I saw no mark of human footsteps on the same 
route ; I knew that the animal was blind in one eye, 
because it had cropped the herbage only on one side of 
its path ; and I perceived that it was lame in one leg 
from the faint impression that particular foot had pro- 
duced on the sand ; I concluded that the animal had 
lost one tooth, because wherever it had grazed a small 
tuft of herbage was left uninjured in the centre of its 
bite," etc. 

If it can be shown that there are two or more persons, it 
follows that all is not one, that all is not God. Accord- 
ing to every scheme of pantheism, I, as part of the uni- 
verse, am part of God, part of the whole which con- 
stitutes God. In all consciousness of self we know our- 
selves as persons ; in all knowledge of other objects. 



APPENDIX. 205 

we know them as different from ourselves and ourselves 
as different from them. God then must be different from 
one part of his works. He must be different from me. 
19. If the Major Term be the Predicate of the Major Propo- 
sition, prove that the Minor Premiss must be Affirmative. Id 
what Figures does this happen ? 

Prove that the Major is Universal in the First Figure, and the 
conclusion Particular in the Third Figure. 

If the Middle Term be the Predicate of both Premisses, prove 
that one of the Premisses must be negative. 

Given the Minor Term the Predicate of Minor Premiss, prove 
that A cannot be a Conclusion. 

Given the Major Term the Subject of Major Premiss, prove 
that A cannot be a conclusion. 
Prove that A can be drawn only in the First Figure. 
Prove that the Minor Premiss cannot be Negative in First 
and Third Figures. 
If the Minor Premiss be E or O, the Major must be Universal. 
Given I as the Major Premiss, determine the Mood and Figure." 
Prove that O cannot be a Premiss in First Figure ; that it can- 
not be the Major in the Second Figure ; or the Minor in the 
Third Figure ; and that it cannot be a Premiss in the Fourth. 
20- Reduce the following to First Figure : 
Every virtue promotes the general happiness ; 
Cunning does not promote the general happiness ; 
.*. Cunning is not a virtue. 
All men are liable to sorrow ; 

Some men are in the enjoyment of great prosperity ; 
,\ Some in the enjoyment of great prosperity are liable to guf 
fering. 
All men are sinners ; 
Some men are not cruel ; 
.*. Some not cruel are sinners. 
Every liar is mean ; 

No mean man should have a public office ; 
.*. No man should be elected to public office who is a liar. 
21. Put the following in the form both of Extension and 
Comprehension : 



206 APPENDIX. 

Deceit, being a sin, will be detected and punished. 
Cause and effect, not being a law of Discursive Thought, 
does not corne within the province of Logic. 

22. Psychology, Logic, Ethics, ./Esthetics, all tend to give a 
power of internal observation and of analysis to the student ; 
and these being all the mental sciences, we may conclude that 
all the mental sciences tend to give a power of internal obser- 
vation and analysis. 

Oxygen, chlorine and steam, etc., are all the gases ; and as 
they are elastic, it follows that all the gases are elastic. 

23. Dr. Reid says, " This simple reasoning, A is equal to B, 
and B to C, therefore A is equal to C, cannot be brought into any 
syllogism in mood and figure." 

The narrative is trustworthy because the author has means 
of knowing about what he writes, and trustworthy 
authors must have means of knowing about what they 
write ; the narrative is trustworthy because it is evi- 
dently sincere and candid, and trustworthy writers are 
sincere and candid ; the narrative is consistent, and 
trustworthy narratives are consistent. 
24:. Elephants are stronger than horses ; 
Horses are stronger than men ; 
.•. Elephants are stronger than men. 

A is greater than B, and B than C, therefore A is greater than 0. 
Plato lived after Socrates, and Aristotle after Plato, and so 

Aristotle lived after Socrates. 
Three-fourths of the fruit in the garden were apples; 
Three-fourths of the fruit were blown down ; 
.*. Some of the fruit blown down were apples. 
25. The fact that I defended him is a proof that I held him 
innocent (stated both as Conditional and Categorical). 

"When about to prove the equality of two given Figures, 
Euclid shows that if the one is not equal to the other, it must 
either be greater or less ; and he points out the absurdity cf both 
these suppositions : 

It is known that a rider proceeding along a road and coming 
to a place where other three roads meet, must have 
taken one or other of the three ; we examine two of 



APPENDIX. 207 

them, and find that he had not gone by them, and we 
at once conclude that he must have gone on the third. 

h i man is not a brute or a divinity, he is capable of making 
progress. 
26. Put the following in form of Sorites and draw it out in a 
series of Syllogisms : 

A demagogue must hold the populace in contempt ; for 
being a favorite with the populace, he must know how 
to manage them, and in doing so he understands their 
weaknesses, and understanding these must hold them in 
contempt. 

1L— EXERCISES AS TO VIOLATIONS OF THE LAWS OF THOUGHT. 
In Notions. 

27- Examine the following : 

A line is said to have length without breadth. There can 
• be no such line ; it is a mere abstraction, a ghost, a 
nonentity ; and all that is demonstrated regarding it 
can have no objective value. 

" What follows from a definition follows in reality from an im 
plied assumption, that there exists a real thing conform 
able thereto. This assumption in the case of the defini- 
tions of geometry is false. There exist no real things 
exactly conformable to the definition. There exist no 
points without magnitude, no lines without breadth and 
perfectly straight, no circles with all their radii exactly 
equal, nor squares with all their angles perfectly right." 

" Concreta vere res sint : abstracta non sunt res sed reruin 
modi ; modi antem nihil aliud sunt quam relationes rei 
ad intellectum " (Leibnitz). 

M A concept cannot in itself be depicted to sense or imagina 
tion." 
28. TJniversals have an existence prior to things and above 
tilings. 

The One, the Good, are the highest realities, are the only 
realities, and the mind is in its highest exercise when 
it is contemplating them. 



208 APPENDIX 

29. Try the following by the Rules of Definition, and amend 

A square is a four-sided figure. 

(Amended) A square is a four-sided rectilinear figure witl 
its sides equal. 

A deer is an animal with branching horns. 

The judicial power is not the legislative. 

A newspaper is a printed paper appearing periodically. 

Words are the signs of thought. 

A general notion is an inadequate notion of an individual. 

Judgment compares notions. 

Conversion is the changing of terms in a proposition. 

Opposed propositions are those which differ in quantity and 
quality. 

Contradictory opposition is the opposition of contradictories. 

A conditional proposition consists of two categorical propo- 
sitions connected with each other. 

A disjunctive proposition consists of two or more categori- 
cals connected by the prepositions either and or. t 

Reasoning is the deriving of one truth from another. 

A fallacy is an unsound mode of arguing. 

Ambiguous middle is a fallacy in which the terms admit oi 
more than one meaning. 

Ignoratio Elenchi is drawing a wrong conclusion. 

Petitio Principii is a begging of the question. 

50. Try the following by the Rules of Division : 
Discursive Thought may be divided into the Term, Judg 

ment, and Syllogism. 
Animals may be divided into Quadrupeds, Birds, Fishes, 
Reptiles, and Invertebrata. 

Literature consists of History, Biography, Tales, Theol- 
ogy, Poetry. 

Notions are Concrete, Singular, and Universal. 

Propositions are Affirmative, Negative, Universal. 

All our ideas must be had either from Experience or a 
priori. 

51. Analyze Pleasure, the Sensation of Heat, the Idea of tna 
Color White, Consciousness. 



APPENDIX. 209 

in Judgments. 

32. Criticise the following : " Every notion holding the place 
01 a predicate in a proposition must have a determinate quantity 
in thought." " TW relation between the terms of a propositioi 
is one not only of similarity, but of identity." " The terms of a 
proposition are of an absolute equality, and all propositions an 
equation of subject and predicate." 

33. What is conducive to happiness is good, and so 
The good is that which is conducive to happiness. 

All equilateral triangles are equiangular, and therefore 

All equiangular triangles are equilateral. 

That God is infinite implies that the Infinite is God. 

We are not entitled to say that because Raphael was the 
greatest painter which Italy has produced, that there- 
fore the greatest painter which Italy has produced wast 
Raphael ; but simply that among the greatest paintem 
which Italy has produced was Raphael. 
3d. Since it is false that all men are liars, its contrary must 
be true, that no men are liars. 

Since it is true that some men are very designing, it cannot 
be true that some men are not designing. 

35. If Alexander was the son of Philip, we can surely argue 
by Immediate Inference that Philip was the father of Alexander. 

In Reasoning. 

36. Are the following allowable, EAI, AEI, EAE? Is 
A A I admissible in Fig. I. ? Or I A I or A E E ? In what Fig- 
ures are A A I and I A I admissible ? 

37. Why is I E O to be rejected ? A person urged that there 
might be a valid syllogism in I E O, and gave the following : 

I Some X is Y; 
E Every T is not Z ; 
O Some X is not Z. 

38. All wise legislators suit their laws to the genius of theil 

nation ; 
Lycurgus did so ; 
.*. Lycurgus was a wise legislator 

14 



210 APPENDIX. 

"Whatever is universally believed must be true ; 

The existence of God is not universally believed ; 
.'. It cannot be true. 

Cloven feet being found universally in homed animals, we 
may conclude that this fossil animal, since it appears to 
have had cloven feet, was homed. 

He must be an atheist, for all atheists hold these opinions. 

You see that men who are indifferent to all religion do not 
seek to compel others to believe as they do ; and as 
this man does not seek to compel others to believe as 
he does, we may conclude that he is indifferent to reli- 
gion. 
30. Liberty is a good thing, provided it is not abused; bu 4 
it is abused, so it is not a good thing. 

All those who say that Logic can teach man to reason must 
approve of Logic ; but as you cannot say that Logic 
teaches man to reason, you cannot approve of it. 

This world would be a happy one if all men were good ; but 
all men are not good, so our world is not a happy one. 

40. Examine the following, both as Categoricals and Condi- 
tionals : 

All must approve of this student who consider him diligent; 
and as you approve of him, you must consider him dili- 
gent. 

There is always discontent in a country when it is ill-gov ' 
erned ; and as there is always discontent in Ireland, we 
may conclude that it is ill-governed. 

Provided the differences between one political party and 
another, and one religious sect and another, are of no 
moment, they ought to tolerate each other : but the 
differences are important, so they ought not to tolerate 
each other. 

41. Honors and rewards by the government or private patrons 
are useless ; they cannot influence the stupid, and men of geniua 
rise above them. 

There is and can be no revelation of His Will by God : for 
if the matter of it cannot be received and comprehended 
by the human faculties, it is no revelation ; and if, or 



APPENDIX. 211 

the other hand, it can be compassed and comprehended 
by the human faculties, it could be attained by them, 
and is no revelation. 
&2. If it be a good thing to have faith, surely he who believes 
la the £oran has faith, and must have a good thing. 

It is absurd to maintain that when we cannot avoid think- 
ing or conceiving of a thing, it must be true ; for some 
persons cannot be in darkness without thinking of 
ghomtSj in which they do not believe. 
45. I think the government should punish this man, as he 
hi told a flagrant falsehood, wh'ch is wrong, and he who does 
w *ng deserves to be punished, aud government is appointed 
f< the punishment of evil doers. 

\4. The Irish are witty, and this man being an Irishman, must 
\ witty. 

Epimenides the Cretan says, that ' all the Cretans are liars ;" 
but Epimenides is himself a Cretan : therefore he is 
himself a liar. But if he be a liar, what he says is un- 
true, and consequently the Cretans are veracious : but 
Epimenides is a Cretan, and therefore what he says is 
true. 
If I buy this piece of land it will be profitable ; if I engage 
in this mercantile speculation it will be profitable ; if I 
buy this house it will be profitable ; and so I may do 
all these and find it profitable. 
To lay restriction on the importation of iron is profitable to 
all home iron masters and iron workers ; to lay restric- 
tion on the importation of linen goods is profitable to all 
in the linen trade ; and so to lay restriction on woollen 
goods, to all who are in the woollen trade, etc. ; and so to 
lay restrictions on all these and other articles will be 
favorable to the nation composed of such traders. 

45. I believe this on the authority of my church, which is 
founded on the Word of God, which all the Church believes in. 

46. It is clear that the United States do not acknowledge 
God as King of Nations, for they have no Established Church. ■ 

Some one proposes what seems a good measure for the 
country at large ; and it is shown that it will cause some 



212 APPENDIX. 

people to grumble and a number of persons in the pub 
lie service to be discharged. 
Our forefathers, the wise and good in former generations, 
all believed this and acted on it, and I am satisfied to 
follow their example. 

47. The theories of geologists cannot be true, for they tend to 
undermine our belief in Scripture. 

48. I charge you with having started this calumny against 
me ; and if you deny it, you must disprove the allegation. 

49. I know that this man, that man, and others, all gained 
large sums at play ; and surely I may do the same. 

I have found on three occasions, when I had a dream of this 
kind, I heard soon after of the death of a friend. So 
when I dream in this way, I expect to hear of a death. 

50. The institution has flourished under these rules ; and if 
would be wrong in any one to attempt to change tbem. 

51. Aut Sirius ardor ; 

Hie sitim morbosque ferens mortalibus asgria 
Nascitur, et laevo contristat lumine ccelum. 
The weather cannot be warmer till the snow is off the 

ground. 
A.S long as the interest of money is so low, trade cannot be 
prosperous. 

52. This story is likely to be true, for I had it from a man of 
fair character, who lived soon after the event (estimated value of 
testimony T 9 7 ), who probably had it from his father (J). 

As each of the witnesses may possibly be wrong, we may 
believe them both to have been in error. 

















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